High altitude flight theory question

[agpilot24]

Let's say we have an electric powered sailplane that climbs at 1,000 feet per minute at sea level(steady state climb) at full throttle. Power out of the gearbox to the propeller is 500 watts.
If we took this model to 30,000 feet, would it still climb at 1,000 feet per minute if we re-pitched the prop to attain 500 watts out of the gearbox to the prop? Assume same prop, much higher pitch. Would different gearing AND pitch be in order? Or, would we need an entirely different prop and gearbox?
For the sake of airframe design, let's assume that the climb speed is the same indicated airspeed for both....although true airspeed will be much higher at 30K(flutter is no issue because of balanced controls and constructed out of unobtanium).
Are there any "short" answers? I do realize that for me to truly understand the dynamics of this will require much reading. Any ideas on books to get me started? Should have finished that AE degree :o
Thanks in advance for your time.
-Jason(foreigner to flight any higher than that tree I just missed ;) )

[vintage1]

I don't know the exact answer to this, but basic physics is a starting point to work out what certianly is not the case.

I.e. we can at least strip the problem down to examining things that may be correct and throw away all the obviously incorrect answers.

Looking at energy and power first, the majority of the power expended by the prop system in lifting a sailplane goes into incraseing the potential energy of the aircraft. Teh force of gravity is not noticebaly less string at 30,000 feet so to a first order it should take the same power to keep the climb going. Assuming we can get similar efficiencies out of the prop system.

What DOES change is the air density - hugely.

What propellors do, is take a cylinder of air approximately equal to the diameter of the prop, and accelerate it to something close to the prop pitch speed.

The thrust generated is the volume of air per second times the speed it leaves the prop times the density of the air - the force being derived from the momentum change of the air. So to maintain thust with thin air, you need more air or more velocity (more diameter, or more pitch) or both. In addition the model needs to fly faster to stay in the air as the stall speed goes up with air density. This leads to the coarse (:)) 'rule of thumb' that a coarser pitch prop is what you put on the front to fly a normal model at higher altidude.

In short, you model has to fly faster to stay in the air, and to get the same climb rate, but it 'feels' as if its wing area has been reduced. So its climb angle will be reduced, its drag reduced and its speed has to go up.

In practical terms what you are probably looking for is a variable pitch prop. Whose pitch speed is a comfortably above best climb airspeed by a small margin, and stays that way as the air gets thinner and the model goes faster.

whether there are 'better' solution are beyond me: But real world propellor driven aircraft can reach 30,000 feet or so. They do not do any more than alter the pitch on the props.

Possibly at extremely high levels and very thin air, you need morre prop diameter as well as the amount you camn accelerate the air to get the thrust is limited by things like the speed of sound - getting ever lower as you get higher - so my tentative suggestions would be to fit a larger propellor to the same gearbox with a very fine pitch at sea level, that coarsens appreciably as ity gets up to speed and height.

But this is running of the edge of my basic science,....so over to the experts.

[Dick Huang]

agpilot24,
What vintage1 says is all true. If we call 300,000 ft a vacuum then no prop will work. I recommed that you put the numbers in Moto-Cal and try them at sea level and 30,000 ft.
Dick Huang :)

[Sail 'n Soar]

Vintage 1 gave the qualitative answer. Aore quantitative approach is to consider the power it takes to fly. Your 500 watts is putting a given amount of thrust at a given speedThe 1000 fpm represents the amount of excess power the product of the two represents the actual amoung of work you are accomplishing with the 500 watts. I'll start by assuming the motor is geared and proped ideally for the specific altitude and flight speed. In that case ideally your prop gear/rpm combo will be doing the same amount of work at 30,000ft. The rate of climg represents the excess amount of work beyond what it takes to fly the aircraft at a given speed and altitude. The air density at 1,000 ft is ~ 2.6 times greater than at 30,000 ft. Thus your plane will have to fly sqrt(2.6), or ~ 1.6 times faster, but the power required to fly varies with the cube of the speed, so that at a given trim, e.g., best L/D, it takes ~4.2 times as much power to fly, which means that your rate of climb will be reduced accordingly.

You can estimate L/D for your model from its glide slope trimmed at best rate of climb. Then given the area and weight you can calculate the amount of power required to fly the plane at sea level. Multiply that by (4.2-1) and divide that by your model's weight to get an estimate of the rate of climb you can expect at 30,000', given the right prop and gear box combo.

[agpilot24]

I'm still a little confused....why would it take so much more POWER to maintain level or climbing flight at 30K'? The air is thinner and the airplane will have to travel through the air faster, but because the air is thinner, the airplane will only "feel" like it is going the same speed as it was down low. Is this correct? I have always thought that the true airspeed increase with altitude was a freebie.
:confused:

[vintage1]

I am confused too.
Sail'n'soar got the first bit rght - about it needing more speed, BUT forgot that in the thinner air, the drag goes down proportionately.

Drag varies with the cube of speed at constant air pressure, it also varies with air pressure.

Also, when doing all the analyses, the amount of power to maintian level flight is very small compared to what is used to climb our models: I got a figure as low as 3 watts per lb I think for a clean slow airframe in level flight.

I.e. in our models about 90% of the power goes into flying fast or climbing - we ought to be able to totter around in level flight at 1/10th throttle on a clean airframe.

[Sail 'n Soar]

Actually, I was half out of it. The L/D at a given trim would be the same, ignoring RE changes. Will sort that out tonight. In that case you can calculate drag D = W/(L/D), so the extra amount of power going into flying the aircraft will be Delta P/P =(1.6-1)*W/(L/D), since the V at 30,000 feet ~1.6 times that at sea level. Off to work now, but will try to clarify things tonight.

[shaneyee]

The short answer to why it would take more power to fly at higher altitude is that your wings are the same size. You have repitched your prop for the higher altitude but the wings are the same. A plane climbs on its wing not the prop.

Shane

[gkamysz]

Jason, are you going for an altitude record, climbing Mt. Everest and bringing models?

Greg

[agpilot24]

LOL Greg!
That would be a real trick....and one heck of a picture--me throwing a model off the top of Everest!
Seriously, I have been exploring the idea of extreme altitude flight. Extreme for models we deal with anyway. What I am having trouble with is how to design a wing that will fly down here, but still work where the air is quite thin. If an airplane is designed to have a best L/D at say 30 knots at sea level, if we take it up to an altitude where TRUE AIRSPEED is 60 knots(although indicated airspeed is still 30 kt), does it still have the same L/D? Reynolds number will be much higher, so do we need a different airfoil? This same concept also applies to propellers, I would guess. To transition from 0-30,000 feet, I'm now thinking that I would need to build a setup having at least a 2-speed gearbox and variable pitch on a seemingly "too large" propeller. A variable diameter prop would be even better. I have to somehow not overload the motor system down low, while also having a way to increase the load quite a bit to get the same amount of power out of the prop up high. Am I thinking in the right direction?

[gkamysz]

All the things you are concerned about are real concerns. A variable pitch prop should be enough. The biggest problem I think will be your prop, nothing off the shelf will work. Variable pitch shouldn't be hard to make. If you really think you need two speeds it would be much easier to switch a battery pack from a parallel to series arrangement.

The questions is, what power source will get you to 30k?

This is a sustancial challange you've set out for.

Greg

[Sail 'n Soar]

If an airplane is designed to have a best L/D at say 30 knots at sea level, if we take it up to an altitude where TRUE AIRSPEED is 60 knots(although indicated airspeed is still 30 kt), does it still have the same L/D? Reynolds number will be much higher, so do we need a different airfoil?

Best thing is to design and fly to max L/D at altitude, the trim for which will be about the same at 1,000 feet. Due to the lower density at 30,000 feet compared to 1,000 feet, at the same trim/angle of attack/CL, the speed at 30,000 feet will be ~1.61 faster. But because of the difference in kinematic viscosity, the Reynolds number at 30,000 feet will be about 75% of that at 1,000 feet. The impact of the change in RE will depend on the size and wing loading of your model. Assuming you design it large and relatively light so that your RE at 1,000 feet is ~ 200,000, then your RE at 30,000 feet will be ~ 150,000.

Taking the Selig S3021 as an example, at least one set of published wind tunnel data gives CD = ~.014 @ CL = .9 at 200,000 and CD = ~.016 @ CL = .9 at 150,000. Thus, the airfoil profile drag is increased by about 15%, CD due to the fuselage and stab will be increased by something of the same order, and the induced drag will be unchanged. That translates to your L/D at altitude being something on the order of 85% to 90+% of the L/D at 1,000 feet. Not much of a change in the grand scheme of things.

Keep you RE at 1,000 feet >100,000/.75, use your favorite sea level airfoil and don't worry about your airfoil selection any further.

In terms of prop choice, choose your motor and prop combo for max L/D cruise at 30,000 feet, throttle back to control current at lower altitudes and you should be OK there as well. This is consistent with full scale engine design, where the stressing condition is often thrust adn SFC at design cruise condition. This almost automatically achieves more than sufficient sea level thrust.