Calculating the Optimum Climb Angle

[Neil Stainton]

I fly electric gliders (see www.eSoaring.net) with a static thrust/weight ratio of about unity, but probably down to about 0.7 at optimum climb angle. Can anyone please help me calculate the optimum climb angle?

I am a very ex aero engineer and am willing to take measurements and do calculations as necessary. The model I am currently flying is a Super AVA, which is based on Mark Drela's well documented Bubble Dancer, so we have some lift and drag data. I have a MicroPower voltage and current logger, a zlog altitude logger and a voice vario, so I can determine real time rates of descent and altitude, and non realtime rates of climb and power usage.

Attempts at experimentally finding the best climb angle have been thwarted by:

- The reducing motor power during the runs, and over subsequent runs.

- The difficulty of estimating the commanded climb angle.

- Varying wind speed & velocity at altitude.

- Varying air conditions - lift and sink.

Thanks in advance,

Neil.

[wcstoddart]

Neil,

Are you interested in maximum climb per unit time or maximum climb angle or maximum climb per watt input? I assume it might be the last from looking at the technical notes at www.eSoaring.net .

As you say there are quite a few interacting variables. A key one will be estimating the propeller characteristics of thrust and torque versus velocity and RPM. I have done some work with Fred Weick's data from the NACA era that I'll be glad to share with you.


best wishes,
Chris

[Neil Stainton]

Thanks Chris. Overall I want the maximum rate of climb per watt input. Currently I am using MotoCalc to get close, then adjusting the prop pitch (usually) so I am consuming the max allowed power on the ground.

The question really related to flying the model with a fixed powertrain to achieve the best possible rate of climb, but if you can help me to optimise the powertrain better than MotoCalc allows that would be even better!

Neil.

[wcstoddart]

O.K. - it's maximize [dz/dt]/[power from the battery]
or
[Flight Velocity*sin(climb angle)*Propeller Efficiency*Motor Efficiency]/[Flight Velocity*Drag Force]
leading to roughly
[sin(climb angle)*Propeller Efficiency*Motor Efficiency]/[Drag Force]

Note: should that be (power from the battery/ kg of model mass)?

I did not see a mention in the rules of a limitation on the propeller. Is a variable pitch permitted - either controllable by the pilot or automatic? If so then the efficiency of conversion of power from the battery could be substantially improved over a fixed pitch propeller. If a variable pitch propeller is not permitted then there still are some techniques for finding a decent match of the propeller with the power train at flight speed. I'll dig out some reference material and send it along.

Another avenue worth exploring is to develop a database of what works well for the winners of contests and then "mine" the data base for the "gold nuggets" of trends.

I generally like to do some of each.


best wishes,
Chris

[Neil Stainton]

leading to roughly
[sin(climb angle)*Propeller Efficiency*Motor Efficiency]/[Drag Force]


I am not sure about the denominator. Most of the power goes into increasing the potential energy of the model, and halving the drag certainly won't double the rate of climb.


Note: should that be (power from the battery/ kg of model mass)?


Yes we are limited to 200W per kg of model mass - with the power level measured on the ground, at full throttle.


I did not see a mention in the rules of a limitation on the propeller. Is a variable pitch permitted - either controllable by the pilot or automatic?


No the prop pitch cannot be adjusted in flight.

Thanks for your input an observations.

Regards,

Neil.

[vintage1]

I don't know the answer, but O know how to calculate it..

First of all work out the best angle of attack - best lift to drag ratio at the lowest drag possible. This will be a shade over stall speed.

Unless the model is going to have power to go fully vertical, this is the airspeed you want.

Pitch the prop for max thrust at that speed.

The climb angle will be a function of excess power over the drag. With a bit of vector math thrown in.

[wcstoddart]

Neil,
you are right, I left out the energy to lift the model mass. I need to work out the fiddly bits of the theory.

Vintage1,
Your comments are consistent with the general practice for "locked up", moderate powered free flight and are likely to be near "spot on" for the case we are discussing here.

Chris

[Neil Stainton]

That is the classical approach Vintage, but I don't think it is correct for high climb angles. My model achieves 800ft to 850ft in the 30 seconds motor run, which works out at a vertical speed of 19mph (28fps) which is over the model's stall speed.

If the model was climbing vertically the wing would have to be at a large negative angle of attack (the zero lift angle), which is quite draggy for most glider sections.

I am almost sure that a better ROC can be achieved by climbing at about 70 degrees. This allows the wing to be flown at an an angle of attack that creates lift, so the lift vector is assisting the thrust, and the wing drag is reduced.

I guess a solution can be approximated using a spreadsheet to calculate the rate of climb for a range of climb angles and a range of angles of attack. As Chris said, the hard thing will be estimating the prop's thrust.

Neil.

[kcaldwel]

This is a standard performance calculation done for all powered aircraft. It's a bit complicated, but is covered in "Airplane Performance Stability and Control" (Perkins and Hage) on P.178 though 182. They even cover the variable engine power, although it was originally for high altitude changes in engine performance.

Best climb rate will usually come at minimum sink speed, but this isn't necessarily true for the high thrust to weight cases like this one. The method they present gives the optimum speed as a ratio to the velocity at L/D max.

The problem is all the confounding factors you listed in your original post. How are you going to fly the optimum speed or angle even if you know it? It will also change with lift and sink. Seems like you might get a feel for it in still conditions, but for a normal day, it is still going to be pilot skill and experience.

Kevin

[vintage1]

That is the classical approach Vintage, but I don't think it is correct for high climb angles. My model achieves 800ft to 850ft in the 30 seconds motor run, which works out at a vertical speed of 19mph (28fps) which is over the model's stall speed.

If the model was climbing vertically the wing would have to be at a large negative angle of attack (the zero lift angle), which is quite draggy for most glider sections.

I am almost sure that a better ROC can be achieved by climbing at about 70 degrees. This allows the wing to be flown at an an angle of attack that creates lift, so the lift vector is assisting the thrust, and the wing drag is reduced.

I guess a solution can be approximated using a spreadsheet to calculate the rate of climb for a range of climb angles and a range of angles of attack. As Chris said, the hard thing will be estimating the prop's thrust.

Neil.

If in the ultimate analysis the wing is jut a drag inducer and you are climbing on teh prop, then the answer is to get the wing to the lowest drag..

There will be an equation that you will have to solve to find this.

Do it in two parts. Look at the vector L/D component of the wing and at the prop thrust vector, and solve for minimum drag per vertical climb rate.

Then prop for best thrust at that airspeed.

I trust motocalc on this..there is certainly a zone where (although possible) the best ROC is NOT vertical, but at 60-70 degrees...increase power and it turns into a vertical climb ultimately.

[wcstoddart]

Neil,

Here are two possible approaches:

John Lowry's Bootstrap Aircraft Performance Technoque
http://www.allstar.fiu.edu/AERO/AirPer-BA.htm
(This method lends itself to using your instrumented model. Lowry addresses the propeller parameters in a manner in much the same way as Von Mises does in "Theory of Flight")

and

Charles Groth - Optimization of Electric Propulsion Systems
NFFS Sympo #40 2007 Pg 51-56
(I've spotted some typos in the later and am redoing the derivations)

best wishes,
Chris

[wcstoddart]

Neil,

A bit more reading leads me to recognize this as one of those "tough questions". Warren F. Phillips, Mechanics of Flight, examines it in some detail.

If the model is climbing with the thrust vector not parallel to the velocity, a most likely situation, then one ends up with only 2 equations and 4 significant and interacting variables (flight velocity, climb angle, thrust, and thrust angle). These variables are in addition to the assumed to be known parameters including parasitic drag coefficient, Oswald's epsilon, total weight, reference area, aspect ratio, and air density. Off course the thrust varies with velocity and to some degree with the thrust angle relative to the climb angle.

One can study the interaction of the parameters by say picking a typical value for thrust, thrust angle, and velocity and determining the lift coefficient and climb angle. This could take a while to figure just what works a bit better.

I suspect that one's time might yield equal or better knowledge in some flying with a data logger in as near as possible neutral air periods such as early morning or late evenings.


best wishes,
Chris

[macboffin]

The problem is compounded by the fact that having got upstairs, you want to stay there, ie best wing and powertrain for climb is not going to be best for L/D and sink rate ; you can only do so much with flaps etc. Regarding "no variable pitch" you might be able to devise a (moulded) prop which would flex and change pitch at different power loadings/speeds.

[deh6]

This thread may be useful--

http://www.rcgroups.com/forums/showthread.php?t=656071&highlight=angle+climb

[rofujiyama]

Hi, Neil,and guys,
I am very intrigued by this. Since Neil has an altitude logger, wouldnt timed power runs of the same duration, and at varying launch angles, and then cutoff and spoiler or crow deplyment, limiting further climbing, give enough data, to determine the best angle to achieve maximum altitude(with various props or powerplants)?
I would initially see, what the trim for the aircraft would be, at full throttle to maintain level flight, to be used as a base line , for the elevator trim during the various launch angles, so as to have a sort of constant to work with.
If you try this, Neil, your results would be very informative for me and my elec. thermal zagi w/folding prop and choked with dihedral and tiny winglets that used to be round and centered over the aileron hingeline.
I really dont have a problem with duration or climbing to glide , but ,very curious , as to to some real data available by your logger and testing. Thanks
Roland :confused: :)