Important: At this time, Mid-February 2012, this article is being updated frequently. If you have questions or corrections you can contact me at kmyersefo@theampeer.org
     For now, the article is only available as this HTML/Web based version, which is not really good for printing. If the article becomes finalized, I will create an Adobe Acrobat PDF version.

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Introduction
Background on Cylindrical Cell Sizing
The Lithium Iron Phosphate Cells from A123 Systems, Inc.
The Cells Being Used by R/C Fliers
My Personal Comments and Observations
Cell Sources & Obtaining Packs
     What's happened to the prices?
Charging the Packs
Balancing the Cells
Lithium iron phosphate battery (Summary)
Rumors and Other Stuff That May Affect the Availability of These Cells
The Drawbacks to Using LiFePO₄ Cells
The Plane
The Battery Pack
Maximum Completed Airframe Weight
Determining the MCA Weight of a Model
Determining the Wing Area
Simplified RTF Target Weight
Onboard Radio System (ORS) Weight
Beginning the Motor Selection Process
     Prop Diameter
     Prop Pitch, Pitch Speed & Minimum RPM
Selecting the Motor

Example 1: Real World Application - Dymond RC Flite 40
Example 2: Proposed Applicaton - 3S ANR26650M1 2300mAh Basic Sport Plane

     All motors and cell chemistries can be used in a myriad of ways to power model aircraft. No one way is more correct than another, as long as it works as desired in the application!
     The type of plane being exemplified here, non-3D aerobatic sport and sport scale, is NOT the extremely popular park flyer. The type of RC, prop driven, plane being described here is typically seen "mixing it up" with glow and gas powered planes at the local RC flying field. It is capable of taking off and landing on the grass of a RC club field.

     There are standards in Lithium based cylindrical cell sizing that are important to know about. There are many different Lithium based rechargeable (secondary) chemistries used in cylindrical cells.
     Many folks are familiar with Ni-Cad (nickel cadmium) and NiMH (nickel metal hydride) cells. Their sizes are commonly referred to with nomenclature such as AAA (triple A), AA (double A), 2/3A, 4/5A, 1/2SC (sub-C) 4/5SC (sub-C), SC (sub-C), C, D, etc. These size designations don't really tell us much about the cell's actual size, except that we are familiar with AAA (triple A), AA (double A), C and D type non-rechargeable (primary) cells that we use in a lot of our portable electronic devices.
     There are several different "Lithium" chemistries that come in cylindrical cells. Their manufactures specify the size in a different way. They use a number such as 26650 or 18650. While at first glance the designations may seem more confusing, these are actually much more useful designations. The first two digits to the far left in the "designation" indicate the approximate diameter of the cell in mm, therefore a 26650 cell has about a 26mm diameter and an 18650 cell has a diameter of about 18mm. The third and fourth digits from the left indicate the approximate length in millimeters. Both of the example cells would be about 65mm long. At this time I am unable to determine what the fifth digit from the left means.
     Using this numbering system, a sub-C Ni-Cad or NiMH might be a 23430 and an AA would be a 14500, just to show how it works. I'm not sure whether those numbers would be "exactly" correct. They are just being used to show how the system works.
     For those who think in Imperial units;
18mm = 0.708661 in. or between 11/16" & 3/4"
26mm = 1.02362 in. or just over 1"
65mm = 2.55905 in. or about 2 9/16"

     I have personally used the ANR26650M1 cells produced for A123 Systems, Inc. for about eighteen months. Besides my personal experience, I owe a HUGE thanks to Charles of Haralson County, GA who is known as everydayflyer on RC Groups. He got me interested in these cells and has been a great contributor to the knowledge base about these cells on RC Groups.
     There is no such thing as an A123 cell. What have been most typically called A123 cells are a form of a lithium iron phosphate cell developed at the University of Texas. Yet-Ming Chiang, at MIT, is said to have improved the cathode for this type of cell for better power delivery and A123 Systems, Inc. holds the patent (currently in dispute) for this improved technology. There are two different cell sizes that are being used in R/C planes as a power source for electric motors.

A123 Systems Inc.
1 Kingsbury Ave.
Watertown, MA 02472
www.a123systems.com
(617) 778-5700

and

A123 Racing (appears to be a division of the above)
12 Avenue E.
Hopkinton, Ma 01748
www.a123racing.com
is marketing the 2300mAh cell to the R/C car community.

APR18650M1 (1100mAh)
Source: www.elektromodely.sk/A123/APR18650M1_2007-05.pdf
Dimensions: diameter - ~18mm; length - ~65mm (~3/4" x 2 9/16")
Weight: ~40g (~1.5 oz.)
Nominal Capacity: 1.1Ah/1100mAh
Nominal Voltage: 3.3V
Recommended Charge Voltage: 3.6V
Recommended Cutoff Voltage: 2.0V
Maximum continuous discharge: 30A (note: that is ~27C)

1.) The cell is cylindrical in an aluminum canister. It has a nominal voltage of 3.3V and a charge voltage of 3.6V. It has a capacity of 2300mAh, and is capable of 30C (69A) continuous discharges and 60C (138A) pulse (10 second) discharges. Each cell weighs 70 grams (2.47 oz). (See specific notes about the APR18650M1)

2.) A special electronic speed controller (ESC) is not needed to run these batteries. The low voltage cutoff should be set to 2.0V per cell or it can be turned off. (KM Note: It is best to fly timed flights with these cells. There is no knee to warn of lowering power. It's a "cliff" and it drops off "right now!")

3.) There are no special instructions for protection during use or charging. Treat it as you would any other battery.

4.) Balancing is an important precaution when using Lithium batteries. Batteries made up of these cells are not as prone to as much individual cell voltage variance as other batteries, but balancing keeps the pack in good health and ensures maximum cycles.

5.) Voltage sag is how much the voltage drops during the course of a discharge. A Nickel Metal battery's voltage sags throughout the complete discharge. A Nickel Metal battery is only operating at full performance for part of the discharge. The batteries being produced by A123 Systems, Inc. show very little voltage sag during the discharge. (KM Note: until the "bottom drops out" at the end)

6.) These batteries have the fastest charge time for any RC battery. They can be charged to full capacity in 15 minutes or less with a charger capable of providing the input amperage and voltage. Charging at these high rates seems to have no effect on the cycle life of the pack.

7.) These batteries are very safe, and abuse tolerant. They have many safety advantages over Lithium Polymer batteries.
     a.) They are not prone to thermal runaway, which is the leading cause of fire in a Li-Po battery.
     b.) They will tolerate some amount of over voltage before failing. These batteries should be charged to 3.6V/3.7V per cell.
     c.) They will tolerate a charge of up to 4.2V per cell with little damage. Charging to 4.2V per cell repeatedly will have negative effects on the pack. Repeated abuse will yield a much lower cycle life, and can result in pack failure.
     d.) They will also tolerate over discharge. A cutoff voltage of 2.0V per cell is recommended, but these cells will charge up even if discharged to as low as 1.50V per cell. As with over charging, it is not recommended to repeatedly discharge below 2.0V per cell, as it will affect the cycle life and could cause pack failure.
     e.) These cells are manufactured with a Laser welded aluminum canister. This helps to prevent damage from physical abuse such as dropping or crashing them. Even with this protective canister care should be taken when handling and using any battery.

8.) These batteries can be stored at any state of charge for short periods of time 3-5 days. They can also be stored safely for long periods of time. At a 50% to 100% state of charge, the batteries can be stored for 6 months. They can be stored for up to 24 months if they are charged to 100% state of charge beforehand.

9.) Up to 1000 cycles can be expected before reaching 75% capacity. In an average RC application, expect to see over 300 cycles before noticing any change in the battery pack. (KM Note: This has been independently confirmed by several individuals.)

10.) The battery can be charged immediately after use.

     I am extremely pleased with the safety, performance, ease of care and charging, fast field charging time and longevity of the ANR26650M1 (2300mAh) cells, previously manufactured by China BAK for A123 Systems, Inc. It appears that Enerland Co., Ltd., which is now a division of A123 Systems, Inc., is now the manufacturer.
     I also like the fact that they may safely be charged in the plane. I am using battery packs consisting of ANR26650M1 (2300mAh) cells instead of large capacity Li-Po/Li-Poly (Lithium Polymer) batteries in my sport and sport scale planes. To understand how I arrived at this conclusion, read my article "Lithium Face Off: A Head-to-Head Comparison of Li-Po, M1/A123 & Emoli." (homepage.mac.com/kmyersefo/temperature.htm)
     I also like the shelf life of these cells. Like Li-Po cells, they will stay charged for a long time while just "sitting around", but unlike Li-Po cells, they do not seem to deteriorate as rapidly over time, loosing performance, as quickly as Li-Po cells.
     I am having great success using ANR26650M1 (2300mAh) cells at about a 35 amp static draw (about 15C) at wide-open throttle (WOT). Seven minute+ flights are the norm for my sport planes using packs made up of these cells. The recharge time, using my Astro Flight 109 charger (unmodified, when charging my 6-cell packs at 7.45 amps [~3.2C]), is between 18 minutes and 22 minutes. The charge time would be shorter if I could get the amps higher! The cells can handle being charged at a much higher rate. The limiting factor in fast charging these cells is the ability of the "charger" to charge at a higher rate.
     To overcome the limitations of a charger, I have been Zip Charging all of my 3S packs, which cuts the charge time to between 10 and 12 minutes at the field.
     The voltage, from the pack into the electronic speed control (ESC), using about a 35 amp static load, averages about 2.85v per cell. When used in this way, a single cell equals about 100 watts in (2.85v * 35 amps = 99.75 watts). Don't confuse watts in (a power in rating) with watts out (a power out rating).
     Powering a sport or sport scale plane at about 100 watts in per pound (1 lb. = 453.592g) usually yields a plane that will give no quarter to the majority of glow and gas powered planes flying at the local R/C flying field.
     To simplify the process, is the reason I have chosen to use the ANR26650M1 (2300mAh) cells at the "fixed" 100 watts in per cell level. The ANR26650M1 (2300mAh) cells can certainly be used at much higher and somewhat lower watts in per cell quite effectively.
     A good example of the 100 watts in would be my Son of Swallow. The power system draws about 35.2 amps when turning a 10x7 Master Airscrew standard wood prop using a 3S "A123" pack for about 302 watts in.

Ken with Son of Swallow

     Keith Shaw is using about 150 watts in per cell for his Crosby CR-4 racer.

Keith Shaw's Crosby Racer

     At the other end of the scale, I have used as little as 25 watts in per cell in my EasyStar RTF with a 2S "A123" pack.
     Also, I am currently using a 3S pack in a parkzone T-28 Trojan at about 65 to 70 watts in per cell.
     Exceptions can be found for everything, but personally, I have found that using them in the 35-amp static draw area gives me the flight time and power I desire for very good performance.
     I have not used the APR18650M1 1100mAh cells, but from the discharge graphs I have seen, they seem to be best used in the 35 watts in to 40 watts in per cell range. This is only speculation on my part at this time.

     The cells are available from many sources.
     Once again, the least expensive way to purchase the 2300mAh cells is as a DEWALT DC9360 36v 10-cell power tool pack from a source on ebay. At this time the DEWALT packs were going for about $100 delivered. (See the pricing and source table below for current pricing.)
     When the prices for the DEWALT DC9360 10-cell packs were rising, they are almost to the point where purchasing single cells was an option. Single cells do require a little different technique than the "tabbed" cells from the DEWALT packs whose information follows. You'll find a "how to" for single, non-tabbed cells at media.hyperion.hk/dn/a123/packassy/A123packassy.pdf.
     Dismantling the DEWALT power tool packs and harvesting the cells is quite easy. This thread on RC Groups by Lucien Miller/aka LBMiller5 shows just how to do it. Mini-How To - Disassembly of a DeWALT 36v Battery. Lucien Miller also has an excellent How To Build a Battery Pack from A123 Cells.
     Sid Kaufman has figured out the "best way" to take these DeWALT packs apart and make various cell configurations for power packs using the cell interconnects already on the DeWALT pack. The interconnects on the DeWALT pack appear to work okay when used at about the 35 amp static draw being advocated here. Easy Packs from DeWALT 36V Packs (A123 Systems) by Sid Kaufman.

     For a while the prices on individual cells was approaching what the cells were "costing" in DEWALT DC9360 packs on ebay. It appears that the supply of DEWALT DC9360 packs is drying up on ebay, and they are now pretty much in the $160 to $170 range with shipping. Meanwhile, A123 Racing, the supplier of the cells to our suppliers has threatened our suppliers with a notice to cut off their supply if they do not use MAP (manufacturer's advertised pricing). In other words, price fixing is in affect on these cells. It is NOT our suppliers' fault!

     As I've noted, by December 2008, the DEWALT 9360 10-cell packs on ebay are once again in the $100 range for delivered packs. Sometimes the best deal involves purchasing two packs at once.

     Sources for individual cells and packs are listed below.

     IMPORTANT NOTE! The following methods are only for those who know what they are doing. Misuse can result in personal and property damage!

     These cells may also be charged using a power supply such as the MASTECH HY3010E, the MASTECH HY3020E for up to 7 cells or MASTECH HY5020E for up to 17 cells.
     For field charging a small, 1200W or 1250W, generator may be used to power the power supply. Also, several Marine/RV deep cycle batteries may be used with an inverter that changes the DC input to AC output for use by the power supply.

     For cell combinations where the pack can be broken into three cells groups for charging (i.e. 3, 6, 9, 12 etc.), a Marine/RV deep cycle battery or two in parallel, to increase the capacity NOT the voltage, may be used to directly charge the 3-cell pack(s) from the Marine/RV deep cycle. A How-To for a 3S pack may be found here. If you understand this set up, then even greater numbers of these "3-cell" packs can be done.
     I have also used this "Zip Charge" method. My experiences are in this article.

     One of the big advantages of these cells is that they are very robust and seem to withstand over-charging and over-discharging quite well. They do not seem to need to be balanced with every charge like Li-Po packs. The individual cells do need to be monitored and have balancing leads on them to balance the pack(s) on occasion using the Astro Flight "Blinky" Battery Balancer for A123 Cells. Here is a thread on RC Groups about balancing these packs - Yet another A123 Thread / Balancing, is it necessary?

     As mentioned before, everydayflyer is an excellent resource for information about these cells. Here is a post that contains links to just about everything you might want to know about these cells.

     David Theunissen, of the UK, has more useful information here.

Quoted and paraphrased from the above source:

1.) LiFePO₄ was developed by John Goodenough's research group at the University of Texas in 1997.

2.) In 2002, Yet-Ming Chiang and his coworkers at MIT (Massachusetts Institute of Technology) reported that they had successfully doped the cathode with appropriate cations¹ - such as aluminum, niobium, and zirconium allowing development to move forward. Products using the doped nanophosphate materials developed by Prof. Chiang are now in high volume mass production by A123Systems and are in use in industrial volumes by major corporations including Black and Decker, DeWALT, General Motors, Daimler, Cessna and BAE Systems among others.

     1. Cations (cat-eye-ons) are positively charged ions. Cations have fewer electrons than protons.

     There has been ongoing litigation between the University of Texas, MIT and A123 Systems, Inc. about patent issues regarding these cells.

     Rick Page of Victoria, BC Canada posted some interesting information on RC Groups.

"A123 says they are producing batteries at their own plants now, but because of the continuing legal actions they are not being more specific.

BAK indicated that they may use their A123 tooling with Phostech electrodes to make an A123 substitute but only time will tell.

All of which should be very worrisome for A123 investors. The industry seems to have decided that their patent may be invalid. The reason for the A123 high current advantage that was stated in the patent has now turned out to be incorrect and their patent may infringe on the one originally issued to U of Texas and now held by Phostech.

Rick."

And

"This is some of what BAK disclosed for their reasons to terminate their contract with A123. BAK is 'the Company'.

Quote:
The agreement with A123Systems, Inc., under which the Company agrees to manufacture products for A123Systems, Inc. according to the specifications furnished by, and using the finished electrodes and other materials consigned by, A123Systems, Inc. to the Company, had terminated on August 30, 2007.
On September 12, 2006, Hydro-Quebec, a Canadian company, and the Board of Regents of the University of Texas System brought a federal patent infringement suit in the United States District Court for the Northern District of Texas against the Company. The Company has an agreement with A123Systems, Inc., under which the Company agrees to manufacture products for A123Systems, Inc. according to the specifications furnished by, and using the finished electrodes and other materials consigned by, A123Systems, Inc. to the Company. The plaintiffs alleged that by manufacturing rechargeable lithium cells for one of the Company's customers, A123Systems, Inc., for use in DeWALT 36-volt cordless power tools manufactured by Black & Decker Corporation, the Company has infringed two U.S. patents owned by and exclusively licensed to the plaintiffs. The plaintiffs seek injunctive relief and damages in an unspecified amount. If the court issues an adverse decision, the Company may be required to pay the plaintiffs substantial monetary damages. The court has not yet issued a decision on this matter and the Company is unable to quantify the extent of any possible award of damages that might become payable by the Company.

Rick"

Also:

     On February 6, 2008, I was made aware that A123 Systems, Inc. had purchased Enerland Co., Ltd of Korea. Enerland, the manufacturer of extremely high quality Li-Po cells used in Polyquest batteries, FlightPower EVO batteries and more, is now a division of A123 Systems, Inc. and is sharing marketing with the A123 Racing division. My research on the Internet showed that the acquisition was completed in August of 2007. This most likely explains who has been manufacturing the cells since China BAK backed out their deal with A123 Systems, Inc.
     FlightPower has also become a share holder in A123 Systems, Inc., Feb. 21, 2008 www.flightpowerusa.com/News/open_article.asp?articleNo=547&parent=front.

     What this all means to us, I am not sure at this time. It seems that the DeWALT packs have been increasing in price on ebay, which may indicate that the supply is getting shorter or that the manufacturing costs have risen. What is actually happening at this time is unknown.

March 16 - GE buys into A123 Systems, Inc.
venturebeat.com/2008/03/05/ge-invests-in-think-electric-car-and-a123

CHRIS MORRISON | MARCH 5TH, 2008

     In two connected investments, General Electric has put $4 million into Think, a Norwegian electric car manufacturer, and $20 million into A123 Systems, which manufactures batteries that are used in the cars.

     Both companies are already well funded. Think has taken over $80 million to date and A123 has topped $150 million (past coverage here). The new investment by GE makes it the single largest shareholder in the latter company.

     On August 8, 2008 A123 Systems, Inc. published their IPO. Think is preparing to roll out the Think City in Europe.

1.) Duration: Flight times for the 2300mAh cells are good at about 100 watts in per cell static. They usually provide about 7 minutes of fully aerobatic flight. That is slightly better than a 25C 2600mAh Li-Po, which should only be run to about 80% of its capacity, giving it a usable capacity of about 2100mAh. Unfortunately the weight penality is noted below.

2.) Weight: A 6-cell pack made up of ANR26650M1 2300mAh cells weighs a bit over 17 oz. with wiring and connectors. A 6-cell 2600mAh 25C Li-Po (equivalent voltage to a 6-cell pack made up of ANR26650M1 2300mAh cells) weighs about 12.25 oz. The Li-Po weight is based on 5S1P Thunder Power eXtremeV2 cells. A 6-cell "A123" pack can be made from a DEWALT DC9360 for about $100 including wire, connectors and node/balance connector. A Thunder Power 5S eXtremeV2 pack can be purchased for about $150 without power lead connectors.

3.) Form factor: There are times when it is much easier to get the low-profile brick-type form factor of a Li-Po pack to fit well into a given plane.

4.) Easy Availability of Li-Po packs: The availability of pre-made Li-Po packs, to power our electrically powered models, is extremely high with many mAh capacities, power ratings and physical form factor choices. They come ready to use.

5.) Ease of charging: With the very large number of Li-Po packs being sold, finding a charger is much easier for Li-Po cells, as well as Nickel type packs.

6.) Ease of motor selection: A majority of power systems, recommended for today's aircraft, are based on Li-Po use and require some serious rethinking when using the cells from A123 Systems, Inc.

7.) Cell voltage difference: Because the single cell voltage of LiFePO₄ is quite different from Nickel based cells and Li-Po cells, direct conversion in existing systems is sometimes difficult.

     Using 100 watts in per cell makes figuring the completed, ready to fly (RTF) target weight very easy. A two pound (32 oz./900g) plane, 2 cells, a three pound (48 oz./1350g) plane 3 cells, etc.
     Using the tables presented here will allow the average modeler to create these types of planes. The tables makes selecting the appropriate power components somewhat easier.

     The first step in selecting an appropriate motor and prop combination is to figure out what props match the airframe and its mission, in this case, sport and sport scale non-3D aerobatic flying. There are many props available from various manufacturers and suppliers. Again, to keep it simple, I use only APC props. I do not use the SF (slow fly) or Pylon props as they are inappropriate for this type of flying. APC props may or may not be the best for a particular application, but they are readily available and work well in most cases.

     In general, typical sport/sport scale planes have a pitch speed ((RPM * pitch in inches)/1056) between 50 mph (80.5km/hr) and 70 mph (112.5km/hr). Using the stall speed and 3.5 times the stall speed, I have created tables that show possible APC props and the minimum required RPM for the appropriate pitch speed for each ANR26650M1 2300mAh cell count and matching airframe combination.
     To learn more about estimating the stall speed and why 3.5 times the stall speed was used to create the tables, read Keith Shaw's ground breaking "Electric Sport Scale" article from the July 1987 Model Builder magazine. It's the granddaddy of all electric flight articles by Keith Shaw. This is the one everyone STILL references to build great electric planes of all kinds.
     WARNING! Do NOT assume that just any of the listed props will work! The target static amp draw is around 35 amps. Always use an in-line power meter such as the Astro Flight Super Whattmeter, or similar device, to measure the actual amp draw. A tachometer will also be needed to measure RPM to calcualte the theoretical pitch speed. I use the Hyperion Emeter because it is both a tach and in-line power meter device with data logging. The Eagle Tree Systems MICROPOWER E-LOGGER & POWERPANEL is another good option, if you have a Windows OS laptop computer.
     When selecting different props to try with a given motor and number of cells, a good motor calcuation program like the FREE Drive Calculator, for Windows, Linux or the Mac operating systems, is ESSENTIAL to help to narrow down the appropriate 35ish amp draw possible prop choices. MotoCalc and ElectriCalc are commercial programs that run on Windows. There are also Web based calculators like the WebOCalc program. To run WebOCalc, click on Software in the menu of the site and then select the program.
     Use the computer software to suggest which props might be pulling 35ish amps static. Purchase a few of the suggested props. Start the static testing of your motor and props with the smallest diameter and pitch suggested by the computer program. USE YOUR IN-LINE POWER METER! Do NOT mount and run props without a power meter! Limit the time the motor is run "on the bench." Keep all bench running only to as long as necessary to collect the data you are seeking. Never run through a full pack on the ground just to see how long the motor will run! Do all prop testing in a safe area and wear protective eye and body equipment. Make sure others are not present in the testing area. Stay away from the front and sides of the prop arc. Always unplug the battery immediately after the data has been gathered. Remember that not all of the props listed will work! The goal is to achieve a motor and prop combination that will draw about 35 amps static on the chosen cell count.

Step 1: Determine the MAC weight - All of the ARF kit parts that might be used in the conversion weighed a total of 1295.2g or 45.69 oz.
Step 2: Determine the Wing Area - The supplier chose not to publish this information. When the ARF kit arrived the wing area was measured and found to be 646 sq.in. or 41.68 dm^2, including the plastic wing tips.
Step 3: Determine the number of required ANR26650M1 2300mAh cells - 45.69 oz. * 2 = 91.4 oz. as the target RTF Weight. 91.4 oz. / 16 oz. = 5.7 lb. .7 is greater than .45, so the number of cells is rounded up to 6.
Step 4: Verify wing area Check Table 2 verify the wing area is in range for a 6 cell pack. Yes, wing area range for 6 cells is 590 sq.in. to 725 sq.in.
Step 5: Select Motor
    A. Determine the largest usable Prop diameter - I attached the landing gear and provided wheels onto the airframe and found that there was clearance for a 13-inch diameter prop. Larger wheels could also be used without the plane "looking too odd", therefore a 14-inch diameter prop is not out of the question.
    B. Select a motor from the 6S suggested motor table -
    This is the hard part! Using the 6S Suggested Motor Table limits the possible choices, but there are still 18 motors listed that might work in this application.
    If the plane has limited clearance for the prop, then the higher Kv motors in this range should be considered. Other than that, the choice almost becomes a "religious" issue. Since the manufacturers and suppliers do not provide much useful information, it is still very difficult to make a logical choice.
    In this group, I own and have both the most expensive AXI 4120/18 motor and the cheapest HXT 42-60/06 (now known as the Turnigy TR 42-60C) motor. In the section Watts In (power in), Watts Out (power out) and Efficiency I note the differences between using these two motors. Is it worth the $100USD difference? Only you can determine that.

    The proposed model, by design, has 416.5 sq.in. of wing area and will be about 3 pounds or less, making it suitable for a 3S ANR26650M1 2300mAh pack. Since it is being specifically designed to use a 3S pack, it has ground clearance to use an 11-inch diameter prop. It will have a WCL factor of 9.75 or less.
    Viewing the 3S motor table shows that I have found 19 possible motors that might work in this application.
    To start eliminating possible motors, I use the table to determine the Kv range for 11-inch diameter props including the NUPDA noted motors that fall within the range.
Kontronik Kora 15-12W, 150g, Kv 920, $127.00
E-flite Power 15, 152g, Kv 950, $79.99
Scorpion 3026-10, 191g, Kv 980, $69.90
Hacker A30-12L, 146g, Kv 1000, $84.99
Scorpion 3020-12, 157g, Kv 1088, $59.99
Hacker A30-8XL, 179g, Kv 1100, $89.99
AXI 2826/08, 181g, Kv 1130 $93.80
Kontronik Kora 15-10W, 150g, Kv 1133, $127.00
Hacker A30-10L, 146g, Kv 1185 $84.99
Scorpion 3014-16, 122g, Kv 1187, $49.99
    The field is now narrowed down to 10 possible motors.
    The two Kontronic Kora's are eliminated because of price and having to purchase them from Canada, as there is no USA distributor. The E-flite Power 15's and the Scorpion 3026-10's Kvs are so low that there is only one possible prop that might work with each one, so they are eliminated. The Scorpion 3014-16 is "light" for this purpose. It is a lot easier to move the battery pack towards the rear of the plane rather than towards the front, in most situations. That leaves the following five possible motors.
Hacker A30-12L, 146g, Kv 1000, $84.99
Scorpion 3020-12, 157g, Kv 1088, $59.99
Hacker A30-8XL, 179g, Kv 1100, $89.99
AXI 2826/08, 181g, Kv 1130 $93.80
Hacker A30-10L, 146g, Kv 1185 $84.99
    There is no usable prop data for the Hacker A30-12L and it also has a Kv that looks to be "out of range" when compared to the other four Kv numbers. The remaining motors are now arranged by price.
Scorpion 3020-12, 157g, Kv 1088, $59.99
Hacker A30-10L, 146g, Kv 1185 $84.99
Hacker A30-8XL, 179g, Kv 1100, $89.99
AXI 2826/08, 181g, Kv 1130 $93.80
    It is now a matter of personal choice. I would use the Scorpion, in this case, not because of price, but because I want to try one of these new motors. A "Hacker person" should probably use the A30-8XL for the added weight and lower Kv, that is, unless they already have the A30-10L, which they might try. The "AXI person" would obviously choose the AXI.

    The same process is used. Using the table, determine 10-inch prop appropitate motors by their Kv numbers including any NUPDA noted motors that fall within the Kv range.
Hacker A30-12L, 146g, Kv 1000, $84.99
Hacker A30-8XL, 179g, Kv 1100, $89.99
AXI 2826/08, 181g, Kv 1130 $93.80
Kontronik Kora 15-10W, 150g, Kv 1133, $127.00
Hacker A30-10L, 146g, Kv 1185 $84.99
Scorpion 3014-16, 122g, Kv 1187, $49.99
AXI 2820/10, 151g, Kv 1200, $85.60
Scorpion 3026-8, 190g, Kv 1212 $69.99
Turnigy 35-42B, 132g, Kv 1250, $25.20
Hyperion Z3019-10, 145g, Kv 1240, $74.95
Hyperion Z3025-6, 186g, Kv 1255, $79.99
    Eleven motors were found that might be of possible use. Now the process of elimination begins. The Kontronic is eliminated because of price and availability. The Scorpion 3014-16's and the Turnigy 35-42B's weight elinimates them for consideration. The Kv of the Hacker A30-12L falls well below the Kv of the other motors. The AXI 2826/08's Kv falls well below the other, better for swinging a larger prop. The list is now narrowed down to five motors, and again arranged by price.
Scorpion 3026-8, 190g, Kv 1212 $69.99
Hyperion Z3019-10, 145g, Kv 1240, $74.95
Hyperion Z3025-6, 186g, Kv 1255, $79.99
Hacker A30-10L, 146g, Kv 1185 $84.99
AXI 2820/10, 151g, Kv 1200, $85.60
    Again, it is a matter of personal preference. If I were to choose between the two Hyperions, I'd probably lean towards the Z3025-6 because of the added weight.
    Keep in mind that the 10-inch diameter props are a second choice over the 11-inch, but they will still work.

    If and when this plane gets off the drawing board, what am I really going to use? I already have a Hyperion Z3019-10 that is sitting in a drawer, therefore, I am creating this plane to use that motor. Ideally, I would use the Scorpion S3020-12, if I were purchasing a new motor for the project.

    By the end of December 2007 I had run across a plane by Fred Reese called the Swallow. I liked its looks and decided to redesign it to the specifications I had noted above for the Basic 3S Sport Plane. I used my "drawered" Hyperion Z3019-10 for the motor, so I was limited to a 10" prop diameter to keep the static current in the 35 amp area.

The Finished SOS for comparison to the Basic 3S Sport Plane from above

Wing area: ~415 sq.in.
Completed Airframe Weight: 20.2 oz./572.5g
3S "A123" pack: 8.48 oz./240.4g
Hyperion Z3019-10 w/harware & connectors: 5.87 oz./166.3g
Onboard radio system components: 4.73 oz./134.1g
Master Airscrew 10x7 standard wood prop: 0.48 oz./13.6g
Ready to Fly Weight (RTF): 39.75 oz./1126.9g
Wing Cube Loading (WCL) Factor: 8.12 (typical sport plane)
Static Amp draw with noted prop: 35.2
Volts under noted load: 8.59
Watts in with noted prop: 302.4
Watts in per pound: 121.7
RPM: 8525
Pitch Speed: 56.5 mph

    The Son of Swallow took to the air in April and has proved to be everything that I "predicted" it to be.

    To learn more about the SOS, its design and flight characteristics, visit this thread on RC Groups.

    I have gathered a lot of information about typical electrically powered sport and sport scale planes and have found the average WCL factor for sport/sport scale planes to be about 8.5 and about 11.5 for Advanced sport/sport scale planes. Those two numbers were used for the recommended wing area ranges in Table 2 and Table 2a.

    The following are some examples of typical ORS system components and their measured weights. The components listed are for example only. The builder of the model must determine which components are "correct" for the specific use and will be SAFE to use. DO NOT skimp on servo power!
    It is not necessary to use digital servos in these types of planes and may even be "undesirable" because of a digital servo's higher current draw.
    I have added a 5% Fudge Factor to allow for Velcro and added wood bits, plus the "stuff that just seems to creep in" and is unaccounted for.
    WARNING! I have not used Hitec HS-225 servos in planes with more than 6S ANR26650M1 2300mAh cells! Whether they are appropiate for 7S through 10S ANR26650M1 2300mAh applications, I have no personal knowledge. 7S and 8S ANR26650M1 2300mAh planes, powered this way, are about equivalent to a .46 to .52 2-stroke glow engine while the 9S and 10S ANR26650M1 2300mAh plaes are about equivlent to a .60 to .65 2-stroke glow engine. Select servos appropriately for those types of planes.

     Watts in is easily measured using an in-line power meter such as the Astro Flight Super Whattmeter. An in-line power meter is an ESSENTIAL tool when using electric motors to power model aircraft! The power in, when talking about electricity, is expressed as watts in, which is equal to the volts in times the amps in. Watts in is used by authors when they give motor power specifications. They tend to just use the term watts without signifying that it is watts in.
     Watts in is also used when designating the relationship between the power in and the RTF weight of the aircraft. (i.e. 100 watts per pound actually means 100 watts in per pound)
     With the proliferation of electric power, there are many more authors writing about it. Unfortunately, some of these authors have absolutely no idea what they are talking about. I have actually seen statements similar to this, "I wanted 1000 watts out for this (insert plane name) project." and then the author gives the volts in and amps in as proof they reached their 1000 watts out goal. Also, unfortunately, their editors have let these statements be published!
     No power system is "lossless." The power going into the system never equals the power going out of the system. The only real way to measure the power out is with a dynamometer. A dynamometer measures torque. The torque measurement can be converted to units of power. Constructing and using a dynamometer for measuring the power out of the electric power system is beyond the average RC modeler's abilities and capabilities.
     Without having a dynamometer available, the power system losses can be estimated using mathematical models. Many of the computer power system simulating programs use some form of these mathematical models to estimate the mechanical and electrical losses in the complete power system.
     The efficiency rating of an electric power system is the power out divided by the power in. The resulting decimal number is than changed to a percentage by dividing the decimal number by 100. This percentage is known as the system efficiency.
     Many manufacturers of brushless motors give an efficiency range for their motors. For some manufacturers, the efficiency number given is absolute fiction.
     In a complete electric power system, the motor losses, mechanical and electrical, are only one type of loss in the system. There are also losses involving the battery, wires, connectors, and ESC. The total power system loss is the significant number and determines the power out. Almost all of the power system's losses involve electrical or mechaincal energy being changed into heat energy. The less efficient any part of the power system is, the more heat (power loss) it generates as the power level is increased.
     Motors and electronic speed controls that are well designed and manufactured have lower losses than those with an inferior design or poor manufacturing quality control. That means that the "better" ones cost more. Larger diameter wire and shorter wire length also reduces losses in the wire. Good connectors have less resistance, therefore they have less power loss than poor connectors.
    The propeller (prop) efficiency must also be taken into consideration when examining a possible power system for use in a given project. Prop diameter has the largest affect on prop efficiency. It is possible for a power system that is electrically less efficient to be "better", in certain cases, compared to a more electrically efficient system.
    The larger the prop diameter, the more efficient it is. With the "fixed" input power, that I advocate here, the system that can swing the largest prop at the required pitch speed will produce the most "usable" power out. This has no bearing on how much power is being turned into heat by the electrical components in the rest of the power system.
     I have chosen three power systems using a 6S ANR26650M1 2300mAh pack to illustrate this phenomenon. Drive Calculator was used to generate the following comparisons.

DC data:
the good: AXI 4120/14, Kontronic Jazz 80 ESC, APC 11x5.5E, 563 watts in, 458 watts out, system eff. 81.4%, thurst 2312g, pitch speed 56 mph
the not so good: HXT 42-60/06 (now known as the Turnigy TR 42-60C), BP Hobbies 70-amp ESC, APC 13x6.5E, 555 watts in, 405 watts out, system eff. 72.9%, thrust 2781g, pitch speed 49 mph
     I highlighted the extimated thrust because this translates into swifter takeoffs and longer vertical climbs. That is one way to measure "better" performance. Of course the AXI powered version of the same plane might have a bit higher top speed and some of the inertia would also be translated into the vertical climb. Still, the poorer performing, energy wasting Turnigay system has 16 oz. more static thrust, if the Drive Calculator numbers are to be believed.
     Selecting the "correct" AXI shows how it is better than the adequate Turnigy system.
the "correct": AXI 4120/18, Kontronic Jazz 80 ESC, APC 13x8E, 538 watts in, 450 watts out, system eff. 83.5%, thurst 2684g, pitch speed 60 mph
     With a thrust difference of only 100g (3.5 oz.) and a pitch speed over 10 mph faster, it can be seen that when the more efficient electrical system is matched with a more efficient prop (i.e. larger diameter), the outcome is the "best" performance at the same input power level.
     These examples illustrate that while the input power remains "fixed", the output power goes up with a more efficient system. The most efficient system can turn a higher pitched prop (in this example) at about the same amp draw as the less efficient system. The higher pitched prop tranlates into a theoretically higher pitch speed, on the same amount of watts in as the less efficient system. In other words, the plane will "fly better."

10/17/07 Real World comparision:
     I compared my HXT 42-60/06 (now known as Turnigy TR 42-60C), BP Hobbies 70-amp ESC, 6S ANR26650M1 2300mAh pack using an APC 12.5x10 pattern prop with my AXI 4120/18, Hyperion 50-amp OPTO ESC, 6S ANR26650M1 2300mAh pack using the same prop. I took five readings for each setup using my Hyperion Emeter. I found a point in the data where the RPM was the same, meaning the power out was the same.
HXT 42-60/06-Turnigy TR 42-60C 17.32v, 35.0 amps, 606 watts in, 7680 RPM
AXI 4120/18 17.55v, 32.0 amps, 562 watts in, 7680 RPM
     The "better" AXI system is taking 44 watts in less to produce the same watts out. That can translate into a longer run time for the AXI or an larger, more efficient props, like the APC 13x10E or APC 14x8.5E, could be run on the AXI at the same watts in level as the Turnigy, thus increasing the power out and flight performance with the larger props.
     There is a $100USD price difference between the two motors. You must decide whether you will be satisfied to pay less and get adequate performance or you'll pay more for better performance or a longer flight time.

     The Wing Cube Loading (WCL) factor is an indicator used for grouping radio controlled miniature aircraft by their possible flight characteristics. Some people feel that it is a better flyability indicator than wing area loading (WAL) expressed in oz./sq.ft. of wing area. The WCL factor, like WAL, has little to do with the aerodynamics needed to get the model to fly at various sizes/scales in real, un-scaleable air.

     For me, the WCL factor seems to be easier to understand and more useful than the more commonly used wing loading.

     The common wing area loading uses the ready to fly (RTF) weight in ounces (oz.) related to the wing area in square feet (sq.ft.). In Imperial units the wing loading is given as ounces per square foot (oz./sq.ft.).

     Using the wing cube loading (WCL) factor, because it is not 'size' dependent, makes it easier to comprehend the flyability of a plane. If a person states that their aircraft has a WCL factor of 8, no other mental calculations need to be performed, That plane will fly in a similar manner to other aircraft with a WCL factor of about 8.

     Using wing area loading (WAL) is a two step process to understand how a given plane might fly. If someone says that their model has a 20 oz./sq.ft. wing loading, then the physical size of the model must be taken into consideration. A plane with a 400 sq.in. wing with a 20 oz./sq.ft. wing area loading will fly very differently from one with a 1200 sq.in. wing with the same 20 oz./sq.ft. wing area loading. Both the wing area loading and the wing area must be known by the experienced modeler to determine the possible flight characteristics using the wing area loading method.

     The WCL factor indicates the relative ease of flying, or skill level, required to fly various RC model aircraft and allows for ability or "flyability" groupings of these aircraft.

     As previously noted, it appears that when two aircraft, with the same wing loading, are sized or scaled differently, they fly differently. A "giant scale" model of about 1200 sq.in. with a 32 oz./sq.ft. wing loading seems to fly, subjectively, much differently, and seems to the pilot, more easily, than a 400 sq.in. model with the same 32 oz./sq.ft. wing loading.

     The wing cube loading (WCL) factor attempts to handle this apparent difference in "flyability" using a mathematical model. The model takes the two-dimensional wing area and changes it to a mathematical equivalent volume. The mathematical volume is not related to the "real" volume of the three-dimensional wing. The WCL factor does not take into consideration the actual airfoil or aerodynamics required to get the plane to fly at a given size or scale in "real" air. It simply applies an ease of flight FACTOR for grouping and comparing aircraft by possible flight characteristics.

     We create useful mathematical models to help us understand many things. Electrically powered model builders and fliers are aware of and use these types of mathematical models a lot. An example would be when trying to determine the power loss through an electrically powered motor system. Factors such as Io, Rm, Kv, amps and volts are put into a mathematical formula/model to give an answer that approximates what the output power might be.

Here is an example:

     If a model's ready to fly (RTF) weight is 60 ounces and it has 500 sq.in. of wing area, the WCL factor = 60 oz. / ((500 sq.in. / 144 sq.in.)^1.5)
     The 500 sq.in. is divided by 144 sq.in. because there are 144 sq.in. in a square foot. The result yields the wing area in square feet.
     500 sq.in. / 144 sq.in. = 3.4722222 sq.ft. Raising that result by a factor of 1.5 yields a cubic result.
3.47222^1.5 is 6.47
This is the mathematical model number, or factor, and has nothing to do with the actual volume of the wing.

     When a number is raised to the 3rd power it is called cubing the number, which is the number times the number times the number.

     But why raise square feet to the 1.5 if we want the number cubed?
Raising an already squared number by 1.5 is the same as finding the square root of the original number and then raising that number to the 3rd power (cubing).
The square root of 3.4722222 is 1.86339. When you raise 1.86339^3 it equals 6.47. That is the same result as 3.4722222^1.5 as shown previously.

     The example aircraft then has a wing loading of 60 oz. / (500 sq.in. / 144 sq.in.) = 17.28 oz./sq.ft. and a WCL factor of 60 / (500 / 144)^1.5 = 9.27. It has a flyability similar to others with a WCL factor of 9.27, but will only have a similar flyability to planes with between 400 sq.in. and 600 sq.in. wings having a WAL of 17.28 oz./sq.ft.

     How is using the wing cube loading (WCL) factor, instead of the wing loading in ounces per square foot, useful to us?

     A similarly designed plane of 250 sq.in. is not half the size of 500 sq.in. used for the example. Actually it is only about 30% smaller.

     Notice that the wing area loading of this 250 sq.in. model is a much lighter wing loading than the 500 sq.in. winged example, which has a wing area loading of 17.28 oz./sq.ft. Even though the wing loadings are different for the two models, with the appropriate power system and aerodynamics, the 250 sq.in. plane would have much the same "feel" and flight characteristics as the 500 sq.in. model.

     A 1000 sq.in. example for the same type/task aircraft (about 30% larger), using the same cubic wing loading, yields a RTF weight of (1000 / 144) ^1.5 * 9.27 = 169.64 oz. Its wing loading would be 169.64 / (1000/144) or 24.42 oz./sq.ft. Again, the 1000 sq.in. model would have the same "feel" and flight characteristics as the other two sizes, given the proper power and aerodynamics.

     I believe that the WCL factor is a valid indicator of flight characteristics, even more so than the traditional wing area loading. The three different size examples of the same plane, using wing area loadings of 11.65 oz./sq.ft., 17.28 oz./sq.ft. and 24.42 oz./sq.ft., all would have pretty much the same "feel" to the pilot and exhibit close to the same flight characteristics, but their wing area loadings are very different, especially if the smallest version with an 11.65 oz./sq.ft. WAL is compared to the biggest at 24.42 oz./sq.ft WAL.

     In Getting Started In Backyard Flying by Bob Aberle, Bob chose to group model types using weight, wing area and wing loading. When WCL factor is used instead of wing loading in oz./sq.ft., some interesting things come to light. Bob created several groups (p.64, p.65);

Ultra Micro, Up to 2 oz., wing area 50-100 sq.in., wing loading up to 5 oz./sq.ft.
Sub Micro, 2-3 oz., wing area 75-125 sq.in., wing loading up to 5 oz./sq.ft.
Micro, 3-8 oz., wing area 125-300 sq.in., wing loading up to 5 oz./sq.ft.
Parking Lot & Backyard, 8-14 oz., 300-600 sq.in., wing loading up to 8 oz./sq.ft.
Speed 400, 14 oz. and up, 300 sq.in. and up, wing loading 8-10 oz./sq.ft.
     Here's another way to look at them with one specific example from each group.
Ultra Micro: Lite Flyer, 1.6 oz., 68 sq.in., 3.4 oz./sq.ft, WCL factor 4.93
Sub Micro: DJ Aerotech Roadkill Series, 2.8 oz, 80 sq.in., 5 oz./sq.ft., WCL factor 6.76
Micro: GWS Pico Stick, 7.7 oz., 238 sq.in., 4.7 oz./sq.ft., WCL factor 3.62
Parking Lot & Backyard: Merlin, 17 oz, 511 sq.in., 4.9 oz./sq.ft., WCL factor 2.54
Speed 400: Miss-2, 29 oz., 390 sq.in., 10.8 oz./sq.ft., WCL factor 6.5

     While none of these planes would be considered "hard to fly" by an experienced R/C pilot, arranging them by wing area loading first and then by the WCL factor demonstrates why and how the WCL factor can be useful.
     Examples arranged by wing area loading:
Ultra Micro: Lite Flyer, 3.4 oz./sq.ft
Micro: GWS Pico Stick, 4.7 oz./sq.ft.
Parking Lot & Backyard: Merlin, 4.9 oz./sq.ft.
Sub Micro: DJ Aerotech Roadkill Series, 5 oz./sq.ft.
Speed 400: Miss-2, 10.8 oz./sq.ft.

     If you simply base the relative ease of flying on the wing area loading, then the above arrangement would be from the easiest to fly to the hardest to fly. What is interesting is what happens to this arrangement when the WCL factor is used.

Parking Lot & Backyard: Merlin, WCL factor 2.54
Micro: GWS Pico Stick, WCL factor 3.62
Ultra Micro: Lite Flyer, WCL factor 4.93
Speed 400: Miss-2, WCL factor 6.5
Sub Micro: DJ Aerotech Roadkill Series, WCL factor 6.76

     If you have experienced flying some of these or similar models, you should be able to see that using the WCL factor gives a more realistic idea about the relative ease of flight of the various models.

     For many years I have collected data for propeller driven model aircraft using glow, gas and electric power systems. I have archived and analyzed that data in an Excel workbook with several spreadsheets. The Excel workbook is available and may be downloaded to your computer by clicking here.

     Based on the collected data, I have created the following WCL factor levels. Some planes won't work in a given physical environment, where I've used a physical description, but they fly like others in the level.

     Not all aircraft will fit the title or level grouping I have given. An example that doesn't fit the physical environment is the SR Batteries Eindecker E1 powered by a Zenoah G-26 gasoline engine. In a review published in Model Aviation it had a given wing area of 1700 sq.in. and RTF weight of 16 lb. 13.5 ounces (269.5 oz) for a wing loading of 22.83 oz./sq.ft. and wing cube loading (WCL) factor of 6.64. Therefore, this plane fits in my group called Level 3 (typically Park Flyers), but you'd not fly it in a park! However, the relative ease of flight is very much like a park flyer!

     The levels are purely arbitrary. A plane on the high end of one WCL level will most likely fly in a similar manner to one on the low level of the next higher WCL level.

     For comparison, several WCL factors were noted in "Aircraft Performance Parameters Revisited" by Roger Jaffe, Model Builder, June 1994.

Type of Aircraft Wing Cube Loading Factors
Gliders 4
Trainers 6
Sport Aerobatic 9
Pattern 11
Racers 12
Scale 10-15

     The table also illustrates the trend over the past couple of decades to larger glow and gas powered models. Since the data was mostly collected from modeling magazines, and the magazines reflect the "current trends", there are few reviews of the more "typical" .20-size to .60-size glow planes.

     There is also a hint, in my collected data, of a Level 0 emerging. I only have data for one plane, but have read about others that might become part of this new level. The Level 0 planes might be called "Living Room" Flyers.

More Information on wing cube loading (WCL) Factors
MODEL DESIGN & TECHNICAL STUFF: WING CUBE LOADING (WCL) by FRANCIS REYNOLDS , Model Builder - September 1989
3D Wing Loadings: a Better Way to Scale Models and Compare different size models easily by Larry Renger, Dec. 1997

A WCL Factor Calculator

     The wing cube loading (WCL) factor is an indicator of the "flyability" of a given model. It does not indicate the type of performance that can be expected.

     Watts in is a typical indicator of performance. It is a pretty reliable rule of thumb in most cases, when talking about electrically powered planes. I DO recommend it as one indicator of performance, but it is difficult to relate glow and gas powered propeller driven models to electrically powered models using that method. It is also difficult to relate the performance of a model "flying on the wing" to one "flying on the prop."
     Today, we have onboard data gathering systems that can record actual performance such as airspeed in level flight, climb rate and more, yet much of our performance "feelings" about a given aircraft are based on our perceptions of how it is flying based on previous experience with various propeller driven models. There is a tendency to say that one model flies "better" than another based on these perceptions. "Better" is a relative term, also based on perception.
     The following theory attempts to create a performance factor (PF) that can be applied to all types of propeller driven radio controlled models. The method can be used to compare completed and flying aircraft and rank them by "performance." It can also be used to "get a feel for" the performance of a newly completed model before the maiden flight.

A performance factor theory:

     One component of my performance factor theory is the pitch speed to stall speed ratio. It can be equally applied to both glow and gas and electrically powered propeller driven models. The pitch speed (PS) to stall speed (SS) ratio relates the theoretical pitch speed to the theoretical stall speed.

Ratio of Pitch speed to Stall speed:

     In Keith Shaw's ground breaking "Electric Sport Scale" article from the July 1987 Model Builder magazine, he states;

     "The stall speed of our models depends on the wing loading, airfoil choice and surface contour finish, but fortunately is not a very strong function of any of these. At wing loadings of 14 to 25 oz./sq. ft. and the nominal airfoils used in sport scale, an amazingly reliable stall speed estimate is: Stall speed (mph) = 3.7 x the sq. root of the wing loading (oz./sq.ft.)
     In order to just do a nice inside loop, the plane must enter at twice the stall speed. To do clean inside loops, rolls, and other sport-type aerobatics, three times stall speed is needed. Anything over 4 times the stall speed gives 'fighter-type' performance and extended vertical aerobatics."

Some specific examples of pitch speed to stall speed ratios:

Theoretical Pitch Speed (PS) in mph = (Pitch [in inches] times the prop RPM) divided by 1056
Theoretical Stall Speed (SS) in mph = 3.7 times the square root of the wing loading [oz./sq.ft.]

     I have owned and flown the SR Batteries Bantam monoplane backyard flyer. My version used all of the recommended components. It has 210 sq.in. of wing area and weighs 8.3 oz. ready to fly, which yields a WCL factor of 4.71. (Level 2). It has a pitch speed of 16.7 mph and stall speed of 8.83 mph and pitch speed to stall speed ratio of ~1.89. According to Keith's statement, this plane would most likely NOT do a nice inside loop from level flight, and it wouldn't. The plane required a dive to do a nice inside loop.

     My ElectroFlying Fusion sport plane has a wing area of 569 sq.in. and weighs 73.9 oz. ready to fly. The WCL factor is 9.41, which is towards the high end of Level 4, typical sport. It has a pitch speed of ~74 mph and stall speed of ~16 mph with a pitch speed to stall speed ratio of 4.62. Keith's statement indicates that this plane should have "fighter-type" performance, and it does!

     If "flying on the wing" were the only type of flying task to be considered, then this performance indicator would be sufficient to make valid comparisons between performances of various propeller driven models.
     However, there are other tasks asked of propeller driven model aircraft. These tasks rely more on the aircraft "flying on the prop" rather than "on the wing." Flying types that rely more on "flying on the prop" are the limited motor run time (LMR) events for electrically powered sailplanes and old-timers. These types of planes are literally "pulled" to altitude by the prop.
     Another type of "thrust flying" has become known as 3-D. 3-D can be flown with both glow and gas powered planes and electrically powered planes. An appropriately powered 3-D plane can literally hang on the prop in a hover and then pull vertically from that position, like a helicopter.
     In general, both the LMR type and 3-D type aircraft use props with a larger diameter and lower pitch yielding a lower pitch speed to stall speed ratio than planes that "fly on the wing" with about the same wing area. Larger diameter props create more thrust than smaller diameter props, so the perception is that the LMR and 3-D planes have more performance, even with the lower pitch speed to stall speed ratio when they are compared to a similar sized "fly on the wing" plane, which tends to have a higher pitch speed to stall speed ratio.
     Many modelers have converted existing glow or gas powered planes to electrically powered planes. Often they will say something like, "it flew as well or even 'better' as an electric." They also note that they used a .40 2-stroke with a 10x6 prop on their glow version and used an appropriately sized brushless motor on their electric conversion using a 14x10 prop.
     A "typical" .40 glow 2-stroke sport engine might turn a 10x6 prop at about 11,500 RPM. An appropriately sized electric motor might turn the 14x10 at 7000 RPM. The 10x6 at 11,500 RPM has a theoretical pitch speed of about 65 mph, while the 14x10 at 7000 RPM would have a theoretical pitch speed of about 66 mph. The theoretical pitch speeds are about the same. The electric might be perceived to fly "better" for one reason; more thrust from the larger diameter prop. According to my very rough calculations, the 10x6 at 11,500 RPM might be producing about 67 oz. of static thrust while the 14x10 at 7000 RPM could be producing about 85 oz. With the same pitch speed in level flight, the planes may seem quite similar until pulled into a climb. The electrically powered version, with more thrust available, would climb higher or at a greater angle when compared to the glow powered version and thus be perceived as a "better" flying plane.
     It can then be seen that a total performance factor also needs to take "thrust" into consideration to allow for the "better" performance of larger diameter props.
     A thrust to RTF weight ratio is extremely difficult to determine. The prop's physical characteristics, the sea level elevation and the ambient temperature all affect the actual thrust. The static thrust, while somewhat of an indicator of available thrust, is really quite unreliable and varies greatly with the pitch to diameter ratio.
     Here is what Tom Hunt had to say about "thrust" and the thrust to weight ratio. It appeared in his column "Electro-Active: Power system selection: Part 7 - The Propeller", FlyRC, May 2006.

     "... Static thrust is the value (usually in pounds in 'English' unit countries) measured 'on the bench'. The oncoming air-speed is '0'. The number derived from measuring static thrust is a very useful number if you are designing helicopters or '3D' aircraft, but has little bearing on choosing the proper propeller for just about any other model.
     Many 'rules of thumb' have been published over the years for the modeler that predict the performance of the model based on the ratio of static thrust from the prop to the vehicle weight. Some say that you need a minimum of one pound of thrust for every three pounds of vehicle weight just to get a model to fly; one and a half pounds for every three pounds of weight for 'acceptable' performance, and anything above that for aggressive flying. Some state that you need better than 1:1 for '3D' models.
     Static testing of propellers with a pitch/diameter (P/D) ratio of greater than .75 (such as a 12x8) can and often does produce erroneous results. Part of the prop, at even these modest P/D ratios, may be stalled (like a wing that stalls and looses lift) which will show poor static thrust. As the propeller moves forward just a few mph, the prop will become 'unstalled' and produce significantly more thrust. As the P/D ratio approaches 1:1, most of the prop is effectively stalled in the static condition and is characteristically 'loud'.
     Even with the ability to accurately measure the thrust of a prospective power plant, an acceptable value by these rules of thumb alone will not guarantee a good flying model."

     Tom's statements indicate that the thrust to weight ratio is not an accurate reflection of the possible performance, but does have some effect on the total flight performance.
     By integrating the pitch to stall speed ratio and the thrust to weight ratio, I have created a Performance Factor (PF) that appears to apply reasonably well to propeller driven models.
     I created a spreadsheet using many of the planes I've built and flown, so that my firsthand knowledge could be used as to their perceived flight performance in relationship to one another. The spreadsheet is available for download at performancefactor.xls. It was revised with the updated theory on June 29, 2008.

     My first attempts to create a useful model for a Performance Factor (PF) did not work out very well. My Multiplex EasyStar kept coming out in the middle of the performance range, when it actually has almost the least perceived performance of all of my planes. The problem was that the EasyStar has a high theoretical pitch speed that it can NEVER reach because of its design, approximately 48 mph! The high PS relative to the low stall speed (SS) gave it a high pitch speed to stall speed ratio.
     When I tried using just the prop diameter, because it has the largest influence on thrust, as a part of the total Performance Factor, the EasyStar's relative performance continued to be higher in my list of planes than it should have been.

     In the February 1994 issue of Model Airplane News, Mitch Poling, in his article "New Thoughts on Gearing" provided the following,

    "My equation for thrust: (Mitch's not Ken's KM)
Thrust (ounces) = PxD³xRPM²x1.0xl0^-10
Note: P = pitch in inches; D = diameter in inches.
The 1.0 is a 'form factor' and can vary from .8 to 1.4, depending on the prop blade shape; 1.0 is an average value."

     At that time, I felt that it didn't do a very good job of predicting the static thrust, because there was a variable in the formula that depended on the type/brand of prop, and of course did not take into account any of the other variables that affect a prop's static thrust. It languished in my memory for the next almost 15 years.
     Since I didn't want "real" static thrust numbers, I decided to give Mitch's formula, without the "form factor", a try as part of my total Performance Factor. After trying various iterations of several formulas, my planes were finally placed, mathematically, in my actual perceived performance order.

     I found that I did need a "form factor" to allow my planes to be aligned more closely to my perceived performance. Actually, my form factor consists of two parts. Part one is the diameter in inches divided by the pitch in inches and part two is multiplying the whole formula by 0.5. I derived the 0.5 after looking at a lot of props and comparing the predicted thrust to the numbers that I was getting using this formula without the 0.5 factor.
     It is important to note that the following is NOT a very good static thrust predictor. It sometimes comes pretty close, and sometimes not close at all! The only reason I'm using it is that it provides a "form factor" to the formula to make the Performance Factor (PF) work.

     Ken Myers' thrust formula, used as part of the total Performance Factor.

Thrust (ounces) = Pitch (inches) x Diameter³ (inches) x RPM² x (Diameter (inches) / Pitch (inches) x l0^-10 x 0.5
i.e. a 12x9 prop at 7000 RPM
Thrust = 9 x 12³ x 7000² x (12/9) x l0^-10 x 0.5
Thrust = ~50.8 oz. of static thrust
Drive Calculator predicts 1402g or ~49.5 oz.

     The thrust to weight ratio is the Thrust in ounces from the above formula divided by the RTF Weight in ounces.

My "Original" Total Performance Factor:
     Performance Factor = pitch speed to stall speed ratio times thrust to weight ratio.

     Near the first part of June 2008, it became very apparent, while testing some K2 Energy 26650 lithium iron phosphate cells (see K2 Cells) that the pitch speed to stall speed ratio was the dominant part of the equation. I found that by squaring the pitch speed to stall speed ratio, all of my aircraft lined up exactly as I perceive them to perform.

My "Latest" Total Performance Factor:
     Performance Factor = (pitch speed to stall speed ratio)² times thrust to weight ratio.

An example of the Performance Factor:
Hangar 9 FuntanaX 100 from my archived data

Photo from Horizon Hobby Web site

What can be learned from the above data?

1. The glow versions might be perceived by the same pilot as slightly "easier" to fly based on the WCL factor. The difference in WCL factor is quite small, so it is also possible that the same pilot would not notice any difference in the "flyability" of the three versions.
2. Based on the pitch speed, the 2-stroke and electric might appear to be flying at about same speed in straight and level flight, while the 4-stroke version would appear to be about 1/2 that speed. It is not "normal" to fly this type of plane in straight and level flight too much, so difference might not be perceived.
3. The Performance Factor (PF) indicates that the same pilot might perceive 2-stroke and electrically powered versions of this plane as having much better performance than the 4-stroke powered version.

     The following shows some of my planes sorted by their performance factors. The sorting is very close to what I believe their perceived performance to be in relationship to each other.

     The following reflects the data I've collected to date for the PF levels in the various WCL Factor levels.

     All of the data can be down loaded as an Excel spreadsheet at metricnewtheory.xls

     This section has been moved to its own article.

Kv Article

The PDL = RTF weight in ounces/prop disk area in sq.ft.
i.e. 60 oz. RTF weight with a 10 inch diameter prop
A diameter of 10 has a radius of 5, 1/2 the diameter
5² = 25 * Pi = 78.54 sq.in. / 144 sq.in. (a square foot) = 0.545 sq.ft.
60 oz. / 0.545 sq.ft. = 110 oz./sq.ft. of prop disk area.

BEC (Battery Eliminator Circuit): an electronic circuit/power supply that eliminates the need for an onboard NiCad or NiMH battery to power the receiver and servos. The usual type, which is built into an electronic speed control (ESC), is known as a linear BEC. There are also switching, external BECs. For both types, as the applied voltage increases (more cells in the motor battery) the ability of the BEC to supply the correct voltage to the receiver and servos goes down. In general, a linear BEC is limited to 10 volts in and three servos. It is VERY IMPORTANT for the user to follow the ESC manufacturer's recommendation when using built-in BECs! If the BEC part of the ESC "dies", the onboard radio becomes nonfunctional resulting in a crash with possible personal or property damage.
     Switching type BECs are designed to handle higher cell and servo counts. Typical examples include the Kool Flight Systems Ultimate BEC and Castle Creations CC BEC. There are many, many more on the market.
     Some manufacturers have started including a switching BEC built into the ESC. The Jeti Spin series, Hyperion Titan "PSB" and "PSW" series and some new ones from Scorpion. Horizon Hobby has the E-flite 40-amp and 60-amp units with switching BECs.
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Brushless Outrunner Electric Motor: A type of brushless electric motor that spins its outer bell of magnets around its windings on a fixed stator. As a group, they tend to have a lower Kv (RPM/v) than inrunners. That means that with same applied voltage, outrunners turn more slowly than inrunners and produce more torque. An outrunner is used for directly turning propellers without the extra weight of a gearbox to get the desired torque.
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C C is the cell capacity in Ah (amp hours). The ANR26650M1 2300mAh cell is said to have a capacity of 2.3Ah (2300mAh). A discharge rate of 15C means 15 times the C rating of 2.3Ah = 34.5 amps.
C is also used when describing the charging rate. If an ANR26650M1 2300mAh cell is charged at a 4C rate that would be 4 times 2.3Ah = 9.2 amps.
Charge Rate-Time in minutes-amp charge rate
1C-60 minutes-2.3 amps
2C-30 minutes-4.6 amps
3C-20 minutes-6.9 amps
4C-15 mintues-9.2 amps
5C-12 minutes-11.5 amps
6C-10 minutes-13.8 amps
etc.
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ESC (Electronic Speed Control) is the electrical device that allows the motor to vary its RPM. It varies the RPM by switching the motor from full on to full off at a very high rate. When the throttle is "wide open", or off, there is no switching going on. The switches (FETs) remain on all the time at "wide open" throttle and closed at no throttle. At partial throttle, the RPM is being varied by how long the switches are allowed to stay on over time. Since the FETs are a switch, there are only two states for it, on or off. Everytime the switches are in the on state, the motor is trying to draw the same amount of current as the "wide open" throttle position. If an inline power meter is used with the throttle at partial throttle, it appears that the motor is drawing less amps than at full throttle. Because the switching is so fast, the meter cannot display what is actually going on and gives an average power reading in volts, amps and watts. An ESC does NOT act like a water valve which restricts the water flow physically! Early speed controls, for brushed motors, acted somewhat like a water valve. They had a wiper arm on a variable resistor that was moved by a servo, thus restricting the flow of current by increasing the resistance in the circuit. Yep, they could get very hot.
     The most important thing to remember about an ESC is that it is switching on and off and the current is not being restricted (While not exactly technically true, it is good enough to think of it like that). Do not think that you can use partial throttle to control the current. It just doesn't work that way.
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ANR26650M1: A type of lithium iron phosphate secondary cell marketed and manufactured by A123 Systems. It is designated as a 26650 size cell. The charged resting voltage appears to be between 3.6v and 3.7 volts.
Dimensions: diameter 1.045 inches (26.5mm), length of 2.6 inches (66mm), weight: ~75g/~2.6 oz., capacity: ~2300mAh
It has the ability to be charged very quickly. It is encased in a metal enclousure. It does not appear to ignite or "burn". It has a lower energy desnsity than lithium polymer (Li-Po/Li-Poly) cells of the same capacity.
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Sport Plane: any type of fixed-wing model aircraft that does not resemble a specific full-scale aircraft.
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Sport Scale Plane: any type of fixed-wing model aircraft that resembles a specific full-scale aircraft but without all of the details of a true scale model.
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