Recommend

This article by Stefan Vorkoetter originally appeared in the August 2004 issue of
QuietFlyer
magazine and is reproduced here with permission.

Electric Flight Rules of Thumb

I've been writing this column since late 1999, and over the years, have mentioned many rules of thumb. A reader recently asked if these were all written down in one place, so I thought this would be a good opportunity to do exactly that, revise some of the older ones, and see how they work together. None of these rules, used by themselves, will guarantee a good performing airplane, but taken together, they almost ensure it.

Power Systems

Probably the most used rule in the history of electric flight is one originated by well known electric flight guru Keith Shaw. The rule states that for reasonable sport performance, a plane's power system should draw at least 40 to 50 Watts per pound (W/lb) of airplane. For good aerobatics capabilities, 70 Watts per pound is more suitable. These figures are in terms of motor input power (Watts = Volts x Amps), and assume a motor efficiency of about 75%, which was typical of a good cobalt motor when this rule was suggested. With a modern brushless motor operating at 85% or better, this can be changed to 35 to 45 W/lb for sport performance, and 60 W/lb for aerobatics.

Rules of Thumb

It is a well established, yet incorrect, belief that the term "rule of thumb" comes from 15th or 16th century English common law. Supposedly, the law allowed a man to beat his wife with a stick no larger in diameter than his thumb. I did some research (mostly by looking at other peoples' research) and found that this was simply untrue, although there are apparently one or two 19th and early 20th century American cases where this alleged rule was applied.
The term was apparently used longer ago than even the 15th century to refer to tradesmen who knew their craft so well, that they would often dispense with measuring devices such as rulers, and just use their thumbs to make accurate measurements (thankfully, they didn't have power saws in those days). Hence, they used a "rule of thumb" instead of a "rule of wood".
This origin of the phrase also makes more sense, since a rule of thumb is not a strict dictum, but just an approximation or suggestion.
I propose that we collectively start a legend that the term comes from the radio control hobby, where many of us fly our rule-of-thumb-designed models with our thumbs.

Another early electric flight rule is that the power system (propeller, gearbox, motor, speed control, and battery) should account for about 50% of the total ready-to-fly weight of the aircraft. This rule, based on the technology of the 198os and early 1990s was intended to help ensure adequate power and duration. Modern nickel metal hydride (NiMH) cells have about twice the capacity for the same weight as the cells available then, and lithium polymer (LiPoly) cells are much lighter yet. Similarly, most brushless motors are lighter than a brushed motor of the same power output. This means that the same performance can be achieved with a power system that represents 25% to 40% of the ready-to-fly weight.

Batteries

A number of years back, former Demystifying Electrics columnist Matthew Orme proposed a simple rule for sport model battery packs: there should be approximately one nickel cadmium (NiCd) cell for each 50 square inches of wing area. This rule was intended for models powered by Sub-C sized cells, and if I remember correctly, either the 1900SCRC or RC2000 were the state-of-the-art at that time. Having chosen the battery pack, one could then apply the other rules to choose the motor, gearbox, and propeller.

A suggestion for full-throttle current draw was that models powered by Sub-C sized cells should draw about 25 Amps, and those powered by AE or AA cells should draw about 10 Amps. The 25 Amp limit was to ensure adequate flight duration, whereas the 10 Amp limit was to prevent cell damage. Modern 3300mAh NiMH Sub-C cells can provide the same durations at 40 Amps, although the smaller cells are still best kept at 10 Amps. LiPoly cells have specific current limits suggested by the manufacturer.

Propellers and Gearboxes

Choosing the right battery and motor will not guarantee a plane that performs well (or even flies at all). Having determined the required power level, an appropriate propeller and possibly a gearbox must be selected to turn that motor output power into something that can move the plane.

The first rule in this area concerns pitch speed, which is the speed that the propeller would move through the air if the air were a solid material. It is approximately the speed that the air leaves the back of the spinning propeller. The rule states that the pitch speed should be about 2.5 to 3 times the aircraft's stalling speed (the speed below which it cannot fly - more on this later). Pitch speed in miles per hour is equal to rpm x pitch x 0.000947, where pitch is measured in inches. If the pitch speed is too low (i.e. much less than 2.5 times the stalling speed), then the propeller becomes inefficient at high speeds. If it is too high, the propeller is inefficient at low speeds.

The rule needs to be modified somewhat for non-sport models: electric sailplanes should have a pitch speed of 2 to 2.5 times the stall speed, and 3D models about 1.5 to 2 times the stall speed.

Another factor is static thrust. This is the amount of pull that the power system provides when the plane is stationary. In general, a model should have static thrust of 1/4 to 1/2 of the plane's weight. Sailplanes that are to make rapid high-angle climbs benefit from higher thrusts, as do 3D models (which require thrust greater than weight in order to be able to hover).

Keep in mind that what really matters is the thrust provided when the plane is moving, but this is hard to measure. Thus, any rules regarding static thrust should be used in conjunction with the pitch speed rule appropriate for the model.

Often, with a given motor and battery, it is not possible to produce the desired combination of thrust and pitch speed, in which case adding a gearbox can help matters by allowing the use of a larger, more efficient, propeller. Of course, there is a rule of thumb that can be used to select the right propeller for a given gear ratio. First, choose the direct-drive propeller that gives an appropriate pitch speed. For example, for a particular high-revving motor, this might be an 8x3. Multiply the diameter by the square root of the gear ratio, and multiply the pitch by the gear ratio. For example, if using a 3:1 gearbox, the 8x3 propeller would become a 14x9. This will allow the motor (not the propeller) to turn at the same rpm, produce the same pitch speed, and far more static (and in-flight) thrust.

A final rule regarding propellers for sport models is that the diameter to pitch ratio should be somewhere between 2:1 and 1:1 (for example, 8x4, 8x5, 8x6, 8x7, and 8x8 fall into this range). Somewhere in the middle is usually best. Used in conjunction with the previous rule, it lets you choose an appropriate gear ratio.

Motor Timing

Like a gasoline engine which has to have the relation between the piston movement and the spark plug firing properly set, a brushed electric motor requires the brushes to be properly positioned relative to the magnets for optimal operation for the conditions (voltage, current, and load).

The simplest method, known as the 10% rule, was suggested by Bob Boucher of Astroflight. First, adjust the motor to neutral timing by running it with no propeller while measuring the current, and turning the end-bell until the current is minimized. Next, rotate the end-bell opposite to the direction of the motor's rotation until the no-load current increases by 10% of the expected full-load current.

This is not a 100% perfect method, but then few rules of thumb are. It will however get you close enough for all but the most demanding purposes.

Aerodynamics

Earlier, we talked about pitch speed versus stall speed. How do you find out the stall speed? Using a rule of thumb of course. A plane's stall speed in mph is approximately equal to 4 times the square root of the wing loading in ounces per square foot. This rule applies to both models and full scale aircraft. For example, my Sig LT-25 has 5 sq.ft. of wing, and weighs 105 oz, for a wing loading of 21 oz/sq.ft. This gives a stall speed of about 18 mph. A full scale Cessna 152 has 160 sq.ft. of wing, and weighs 1,670 lbs (26,720 oz) fully loaded, for a wing loading of 167 oz./sq.ft. This would put the stall speed at 52 mph (the actual stall speeds are 55 mph flaps up, and 49 mph flaps down).

Wing loading itself is not sufficient to indicate how a model will fly. The size of the aircraft has to be factored in (a model with the 167 oz./sq.ft. wing loading of the full scale Cessna 152 would fly like a brick). A measure that is indicative of flying qualities is cubic wing loading, which is computed by raising the wing area to the 1.5 power, and dividing by the weight (if your calculator can't do powers but has a square root key, first cube the wing area by multiplication and then take the square root). Table 1 shows some typical cubic wing loadings for various classes of aircraft.

Type of Model

Cubic Loading (oz./cu.ft.)

Sailplane or Park Flyer
5 to 7

Trainer
7 to 13

Sport
13 to 20

Pylon
20 to 30

My LT-25 has a cubic wing loading of 9.4 oz./cu.ft. which puts it in the trainer category. A full scale Cessna 152 has a cubic loading of about 13 oz./cu.ft., which puts it at the high end of the trainer category (not surprisingly, it's one of the most popular full scale trainers).

Miscellaneous

There have been a few rules of thumb over the years that don't fall into any particular category.

Electric model power systems can generate a lot of heat, and unlike in a glow powered model, the heat isn't all generated up front out in the breeze. This necessitates cooling air inlets and exits. Because the air expands as it is heated, and to ensure that all the air coming in can get out, the total area of the exits should be about three times the area of the inlets. I don't always follow this rule, but it's a good idea to do so in high power models.

As a modeler in the northern half of North America, there are times of the year where I fly my models off of snow. As a result, I've done a lot of experimenting with skis, and have come up with a rule that states that there should be about 14 square inches of ski per pound of model weight (or slightly less than one square inch per ounce). This size minimizes the aerodynamic effects of the skis, yet holds the model up on most snow surfaces.

Finally, none of these rules will do any good if you crash the model because you can't tell which way is up. From both my experience and that of other modelers, I can safely say that it can be easy to lose orientation of the model, and then crash it because you've got up and down mixed up. The best cure for this is a color scheme that is light on top and dark on the bottom. This is in agreement with our experiences that it's generally darker underneath objects. All-white or transparent schemes can be very aesthetically pleasing, but hard to fly.

Wrapping Up

These are most of the rules of thumb that I have made use of during my electric flight career. Keep in mind that they are not hard and fast rules. Some can be ignored in some cases. Others are almost essential to follow, but following them doesn't guarantee success. However, used together, they can go a long way toward achieving electric flight bliss.

Subscribe

Recommend

This article by Stefan Vorkoetter originally appeared in the August 2004 issue of
QuietFlyer
magazine and is reproduced here with permission.

Electric Flight Rules of Thumb

Power Systems

Batteries

Propellers and Gearboxes

Motor Timing

Aerodynamics

Miscellaneous

Wrapping Up

Other Articles of Interest

Subscribe

Recommend

This article by Stefan Vorkoetter originally appeared in the August 2004 issue of QuietFlyer magazine and is reproduced here with permission. Electric Flight Rules of Thumb

Power Systems

Batteries

Propellers and Gearboxes

Motor Timing

Aerodynamics

Miscellaneous

Wrapping Up

Other Articles of Interest

This article by Stefan Vorkoetter originally appeared in the August 2004 issue of
QuietFlyer
magazine and is reproduced here with permission.

Electric Flight Rules of Thumb