How do we calculate range and endurance of an RC plane?

[Keat]

Hey guys I have to calculate the range and endurance for my electric RC planes, but I can only find equations for planes that use fuel.

[MCarlton]

You can make a rough calculation by measuring the current draw at cruise throttle, and dividing the capacity of the battery in mAh by that figure;

Thus - 20A current, 2000mAh capacity = 0.1hrs = 6 minutes

Then, make a rough calculation on flight speed based on prop pitch.

for example, a 6" prop at 10000RPM = 56.82mph

Take a bit off that (say 15%) for prop slip and inefficiency and model drag

Airspeed = 48mph
Motor Run = 6 minutes

48mph / 60 = 0.8mile/minute

6 mins motor run x 0.8 mile/minute = 4.8 miles

So, on a model with a 6" pitch prop, pulling 20A at 10,000RPM, with a 2000mAh pack, your range is 4.8 miles, at a speed of 48 mph.

[vintage1]

Endurance is easy. Go for about 13W/lb level flight and that with the battery capacity and voltage will give you the answer.

Range is more tricky, since it depends on the lift/drag curve and the windspeed.

[JetPlaneFlyer]

Then, make a rough calculation on flight speed based on prop pitch.


You cant calculate maximum speed (even roughly) by prop pitch alone. If it was this simple then you could go ever faster simply by increasing pitch more and more. In the real world it's not that simple; you can put the same power train and same prop with same pitch in two different models and get wildly different maximum speed.
For instance a small lightweight low drag 'hotliner' and a large WWI scale biplane complete with draggy struts and wires.. The hotliner may almost achieve the full theoretical prop pitch speed as per your calculation. The large draggy WWI model might stagger around at a jogging pace... yet by a simple pitch speed calc both should have the same maximum speed.

Ultimately maximum speed is achieved when thrust = drag.. But working out either thrust or drag is far from straightforward, there are many variables. Using empirical data from other similar models is probably the easiest way to do it but there are some computer applications that will work it out too.

Steve

[MCarlton]

Yup, I got it wrong, simplistic thinking. I stand corrected.

[vintage1]

If you know the drag/speed curve, you can pretty much assume that the power train efficiency will be about 50%, and use drag x speed=output power. Or max speed = input power / (2 x drag).

Then prop for around that pitch speed, reducing diameter to keep power correct as you increase pitch.

However that doesn't solve the range problem. You need to do more than that.. Most full size aircraft cruise a little above stall speed. That is where the best drag/speed ratio is.

However, wind makes a huge difference.

[Work in Progress]

However that doesn't solve the range problem. You need to do more than that.. Most full size aircraft cruise a little above stall speed. That is where the best drag/speed ratio is.


Ooh, bit of a sweeping generalisation there.

If you want a marginally less sweeping one, then for most classic-configuration piston-engined aeroplanes, then a good guesstimate for the key indicated air speeds are about 1.3x the 1G clean stall speed for best endurance (or minimum sink with power off) and perhaps 1.4 or 1.5x stall for best range.

But in reality most full size aeroplanes fly a *lot* faster than that, because flying slowly is, well, slow. Generally around 2x clean stall speed is nearer the mark for the economy cruise used by pilots of Cessnas, WW2 fighters, DC-3s, Tiger Moths and the like.

One biggish class exception is jet airliners and U2 / TR1 spyplanes. These often cruise fairly close to clean stall, when they are up at very high altitude where the indicated airspeed is low, yet the true airspeed is high.

[MCarlton]

As I understand it, the maximum range of any aircraft is to fly with the engine at the lowest throttle setting which will allow level flight, hence the aircraft in the lympne trials, which flew on tiny motors which barely allowed the aircraft to fly level.

That might not be the most efficient way to fly in terms of ferrying people around or getting to places, but surely it is the route to the longest flight distance?

So, if I were designing an electric aircraft to fly a long distance (excluding the effects of wind) then to my mind, the specification would be something along the lines of a high aspect ratio powered sailplane, with a small motor, geared heavily, driving a slow turning prop.

Of course, if we could use solar power to keep a lightweight lipo pack topped up, we could probably fly forever?

[Work in Progress]

As I understand it, the maximum range of any aircraft is to fly with the engine at the lowest throttle setting which will allow level flight, hence the aircraft in the lympne trials, which flew on tiny motors which barely allowed the aircraft to fly level.

That might not be the most efficient way to fly in terms of ferrying people around or getting to places, but surely it is the route to the longest flight distance?

As a generality, close but not quite. On your average light aeroplane that would be the correct configuration for maximum endurance, in terms of hours flown. However, but maximum range, in terms of air miles flown, is generally at a slightly higher speed, and a slightly higher power setting. Best endurance is at minimum drag (minimum sink speed on a glider, and lowest power requirement to sustain level flight) whereas best range is found at best lift/drag ratio (best glide angle on a glider, and a bit faster than minimum sink).

So, if I were designing an electric aircraft to fly a long distance (excluding the effects of wind) then to my mind, the specification would be something along the lines of a high aspect ratio powered sailplane, with a small motor, geared heavily, driving a slow turning prop.

That is a good formula for range. The slow prop rotation reduces unproductive power losses through blade drag. High aspect ratio world best at relatively high AoA so a very efficient low speed cruise, at about that 1.4x Vs mark. However, at least as important for range is efficient structural design so that your airframe can carry the greatest possible weight of batteries without shedding the wings.

Of course, if we could use solar power to keep a lightweight lipo pack topped up, we could probably fly forever?

Assuming no cloud, and the right sort of sun angle striking the photovoltaic cells, possibly, and it is in fact being done in experimental pilotless drones. You need to be able to climb most of the day and glide most of the night, so it's not exactly a mission for radio-controlled models.

http://www.dailygalaxy.com/my_weblog/2008/08/green-spy-pla-1.html
http://www.globalspec.com/reference/18737/121073/SoLong-Solar-Powered-Drone-Stays-Aloft-for-48-Hr

Incidentally, one of the most irritating things about maximum range flying with full-size aeroplanes is that the nearer you get to your destination, the slower you have to fly, because your weight is reducing due to fuel burn, so the best speed to fly keeps reducing, so that you carry on flying at the AoA which gives best L/D ratio. It sometimes feels as if you will never get there! However, not an issue with electrics, which don't get lighter as they run out of fuel.

[vintage1]

WIP has summed it up but for one thing. Wind.

If you are cruising at 1.5 x stall and the wind is in your face and also 1.5 times stall, its easy to see that you can stay up till the tank runs dry and not get anywhere.

The maths at this point gets pretty nasty.

Likewise with a tail wind, it may be better to simply stay up at minimum speed just above the stall, and let the wind do the work..

[Work in Progress]

Very true, all of what I said above is for still air.

For maximum range, travelling with any substantial wind behind you, the greater the wind the slower you can fly, down to minimum sink speed in a glider / minimum level flight power in a powered aeroplane.

(Providing you don't oil up the plugs, let the oil get cold, reduce teh revs so far that the alternator drops off line, etc etc, all of which can actually give you quite serious practical constraints in real-life aviation)

Heading into a significant wind, a faster than normal cruise can be necessary. As V1 suggests, the maths of that are best worked out in advance on the ground for various scenarios according to the known characteristics of your specific aeroplane.

Rule of thumb corollary: if you have a headwind it pays fly as low as practically and safely possible (unless you are in a jet, they absolutely guzzle fuel at low level) , and if you have a decent tailwind, then plan to keep on cruise-climbing until you start a long cruise descent. (Because wind speed tends to be stronger the higher you fly, broadly speaking)

[BMatthews]

And let's not forget that we don't fly our models in a straight line from takeoff to landing. To keep them in sight we are constantly flying in turns with short straight sections. Not to mention that a ground based pilot with no instruments or seat of the pants sensing is a very poor judge of speed and attitude and tends to overcontrol more than undercontrol.

So... it all sums up to the answer being "it depends on..... " :D

For duration it's not as bad. Vintage summed it up decently. The amount of watts per lb may vary slightly depending on the style of design. A powered sailplane sort of thing with no dirty parts hanging out in the wind and a bigger and more efficient wing needing less power per pound than a sport style model with all the oddities that it may have. Figure on 13 watts per lb as a ball park beginning and then find tune that number based on your real world results. A closer answer than that would require a lot of info about the model and an accurate calculation of the overall drag coefficient for the design when flying at the minimum cruise vs best lift drag cruise.