Understanding More About Electric Flight

If you read through the "Basics of Electric Flight" it may well have left you wanting more information on how to size engines for speed/thrust etc when designing and building your model plane. So, here is some more great stuff that helpful people in the hobby have taught me, or I have figured out myself.

First some basics:

Pitch Speed

Pitch speed is the speed of the engine/prop combination through the air ignoring drag and prop slippage.

It is simply based on the multiplying the pitch of the propellor, by some number of revolutions for a unit of time.

For example lets say we have a 7x5 prop that we know is being driven at 10,000 rpm then the pitch speed of this model is 50,000 inches per minute (5 from prop pitch multiplied by 10,000 rpm). Once you have this number, conversion to more useful units (such as km/hr or mph) is just a matter of multiplying by the right constant value.

To get km/hr, multiply by 0.001524
To get mph, multiply by 0.000947

So for the example above, with the motor spinning at 10,000rpm, the pitch speed would be 76km/hr or 47mph.

How do you find the RPM? Many motor manufacturers will publish this information with their engine. Some don't. If you don't have published information you can often take an educated guess by looking at the recommended prop ranges for a motor, and assuming that the smallest published size will spin the motor at approximately 85% of kv * volts (so a 2000kv motor with 11.1v, you would expect appoximately 19,000rpm. With the mid range prop you would probably expect around 70% of kv*volts (so 15,500rpm from the example above), and with the largest recommended prop maybe 50-55% (so 12,000rpm from the example).

The best way to find the RPM if it isn't published is to actually measure it with a tachometer.

Finally, if you have an inrunner which is reduced through a gearbox before spinnning the prop you of course need to factor that into your calculations. For example, a 3000kv motor reduced through a 3:1 gearbox has an effective prop kv of 1000.

Thrust

Thrust is a measure of the force generated by an engine/prop combination. Typically it is expressed either in ounces or grams (and those of you that know your SI units of course realise that grams is a mass, not a force, and that this should be more properly described as grams at earth gravity).

Typically a wider diametre propellor will generate more thrust, to a point. Perhaps you have already noticed the tradeoff here. You generally get higher pitch speeds with a smaller prop, but you generally get more thrust with a larger prop.

If you engine doesn't have thrust info provided with it, then you have to figure it out for yourself by measuring it. You'll need some sort of rig that allows you to measure the force the engine generates at full throttle.

Air Resistance/Drag

All things that move through a gaseous medium (ie air) must overcome air resistance. Aircraft are no exception, and they are further affected in this regard because their wings create additional drag.

The important things you need to know about air resistance is that its relationships to velocity is a squared one. That means that if you double your speed, your wind resistance increases by a factor of four. For example if your wind resistance at 30km/hr is 100grams, then your wind resistance at 60km/hr will be 400grams, and at 120km/hr will be 1,600grams.

So How Fast Can a Model Go?

As a model accelerates the amount of drag increases as square of the velocity until either drag equals engine thrust, at which stage the plane will stop accelerating, or the plane reaches the pitch speed of the prop, at which stage it stops accelerating.

It's a bit like gearing in a motor car. In first gear, you are "pitch speed" limited. You have plenty of power to overcome wind resistance, but eventually you reach a point where the engine is at red line and can't (safely anyway) spin any faster. However, it top gear you tend to be drag limited - you accelerate to a point where wind resistance equals the acceleration the engine is providing and you have reached your top speed.

So, the plane's top speed is governed by the lower of the point where thrust and drag intersect, or pitch speed. The graphs at the right will hopefully illustrate this - click on them for a blown up version.

The upward curve is the "drag line", the blue line is the "thrust line" and the yellow line shows the pitch speed. All of these graphs are based loosely around the ewatts R2212 and R2282 1500 and 1200kv motors, with various airframes. For example, I think the first one pretty closely matches my GWS Zero performance.


Choosing the Right Motor/Prop for Your Model

Of course it does depend what your application is. If all you want is thrust for 3d work you are better off getting a lower KV motor and using a larger diametre prop - you are getting the most thrust you can, but typically paying for it with pitch speed (a bit like the 9x3.8 graph). Also, if you have a slow flying airframe you often need to pay for this in terms of drag as you try to go faster.

If you are after speed you have to make a compromise. Clearly you want pitch speed, but you also need enough thrust to overcome air resistance. Normally you have to trade pitch speed against thrust. Sometimes it is easier to lower the air resistance of your model than increase the power (more on that later) if you want it to go faster.

Going Faster

So something I have seen come up on forums from time to time is something along the lines of "this guy showed up with *some fast plane* and blew away my *I thought it was fast plane*. I need to upgrade my power so that I can blow him away."

Okay - time for some hard numbers. As mentioned above, drag increases as a square of velocity. So, to go twice as fast you need four times as much thrust (ignoring pitch speed for the moment).

Let's say for example that you use 700grams of thrust to go 90km/hr, and decide that you need to catch a plane that can fly in level flight at 110km/hr. Take a guess at how many grams of thrust you need (ignoring pitch speed as a limiter for the moment). Got your guess ready? 1050grams. That's right, 50% again to increase your speed by 20km/hr.

Unfortunately Mr Newton has more unpleasantness ready for us. Power is a measure of work over time. If we want to fly twice as fast we need four times as much work done (because we need four times the thrust from above) being done twice as quickly. Yes - you need 8 times the power to go twice as fast. So let's say you were using 200watts to get 90km/hr, what would your power requirements be at 110km/hr? Got your guess ready... were you anywhere near 365watts?

Now - don't despair. A power system upgrade can be a fine thing at times like this, but in many ways you will probably get a much better return by reducing the drag coefficient of your model.

For example, if you reduce your drag coefficient by 20% you can fly a linear 20% faster for the same amount of thrust. So, in the example above you would have almost gotten to 110km/hr without putting in a single watt more of power.

The graph on the right shows another example of this concept.

Now, reducing the drag coeffecient of your model (by reducing wing area, reducing the size of the airfoil etc) is not a free ride by any means. You will end up with a higher stall speed amongst other things making landings and takeoffs more difficult. Your model may well become unstable, you could change the centre of gravity etc. In so many ways you could ruin a great plane - but you could go a bit faster too. So, if you want to make your stryker go faster, as well as upgrading the power, think about how you can reduce the drag coefficient.

What about Weight - Doesn't It Affect Speed?

As best I can tell, weight does not affect straightline speed in an aircraft. It affects acceleration, but not top speed. Obviously if you are fighting gravity then mass does make a difference.

How Do I Tell Whether My Speed Is Pitch of Thurst Limited?

If a model is severely pitch limited it is usally pretty obvious - you push the model to full throttle, it jumps very quickly to a speed but then just stays there. The model has plenty of thrust, but just wont go any faster.

If the model takes a little time to wind out to top speed (not ages, just some time), and can go significantly faster in a steep dive it is probably thrust limited.

If in a dive the model doesn't pick up significantly more speed it might be thrust or pitch limited, but it is so close to pitch speed that it almost doesn't matter (the model doesn't pick up much speed because once the model passes its pitch speed in a diver the propellor starts acting as a brake).

So Is It Better To Be Thrust of Pitch Speed Limited?

It really does depend on application. 3d planes are often pitch speed limited - they usually just want buckets of thrust for unlimited vertical. Most scale models fly best with thrust limited setups in my opinion.


Well I hope you found that interesting. I really enjoyed getting my head around this stuff as I wrote it. Definitely will be including significant drag reduction as part of the elebee project phase III.