Relating propeller thrust, power, and rpm together

[pacgcrosss]

Hi All,

I am involved in a research project regarding electric aircraft. I've done a fair bit of research into this but am having trouble keeping all the different parameters and how they affect each other straight in my head.

Fundamentally I am putting together a model whose parameters I can tweak and iterate through to optimize range, etc. For me, my problem boils down to how much power I need the battery to provide to maintain the thrust required for steady state (cruise) flight.

I've used actuator disk theory to relate thrust to power using this formula (second to last formula of 11.7.3): http://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node86.html

However (and please correct me if I'm wrong) the power in that equation is not exactly the power provided by the battery. To get that I'd need the propulsive efficiency, which includes many variables that aren't relevant to my model (blade pitch, etc.).

Would I be better off using blade element theory? I tried this, and was able to determine thrust in terms of RPM. How can I relate power required from the battery to RPM within the framework of this theory? I know this must depend on many factors such as air density, blade geometry.

Thank you in advance for helping me clear this up in my head.
Pac

 

[Dr.D]

Blade element theory should also provide you a description of the torque required to rotate the propeller, as I recall. The power required, neglecting friction losses, is simply P = omega * torque, where omega [=] rad/s, and torque [=] N.m, gives power in watts. The take into the various losses with efficiency estimates (estimates are usually the best you can get), and you should arrive at the total power required out of the battery.

 

[pacgcrosss]

Blade element theory should also provide you a description of the torque required to rotate the propeller, as I recall. The power required, neglecting friction losses, is simply P = omega * torque, where omega [=] rad/s, and torque [=] N.m, gives power in watts. The take into the various losses with efficiency estimates (estimates are usually the best you can get), and you should arrive at the total power required out of the battery.

Ahh ok thank you! I can see now how to use blade element theory to get the torque. Are there any efficiencies I need to account for other than propulsive efficiency and electrical efficiency? Doesn't blade element theory also provide an accurate number for the propulsive/propeller efficiency, so the only one I would need to estimate would be electrical efficiency right?

Also, I don't see how blade element theory accounts for the lift and drag of the plane as a whole, it only has terms for the individual propeller blades. Intuitively I feel these must affect the amount of power required.

 

[Dr.D]

You must certainly allow for bearing friction in the propeller shafting, the motor, any gearing, etc.

You are correct in saying that blade element theory does not account for lift and drag on the plane as a whole, but that is irrelevant as far as the propulsion system is concerned. Your system definition, for this analysis, consists only of the battery, the motor, any gearing, shafting with bearings, and the blades. The result is propeller thrust. Whether this is sufficient to propel the aircraft is another question, outside the realm of this limited system.

Drag certain affects the amount of thrust required, but not the amount produced. Your blade element analysis is a determination only of the amount produced.

 

[pacgcrosss]

You must certainly allow for bearing friction in the propeller shafting, the motor, any gearing, etc.

You are correct in saying that blade element theory does not account for lift and drag on the plane as a whole, but that is irrelevant as far as the propulsion system is concerned. Your system definition, for this analysis, consists only of the battery, the motor, any gearing, shafting with bearings, and the blades. The result is propeller thrust. Whether this is sufficient to propel the aircraft is another question, outside the realm of this limited system.

Drag certain affects the amount of thrust required, but not the amount produced. Your blade element analysis is a determination only of the amount produced.

Thank you Dr. D, this was very helpful

 

[JBA]

Aircraft are not my specialty, but maybe a work around for your problem, since you do not have drag data for your project aircraft, might be to identify an airplane of similar configuration to your project aircraft and then see if you can get the basic operating specifications for that aircraft, i.e. its cruising speed and horsepower at its cruising speed. Use that for your approximation of your electric motor hp requirements.
Admittedly, this could take a bit of thrashing around; but, as an amateur pilot, I can say, that if you locate a pilot that aircraft, he, or she, can instantly tell the planes cruising rpm. Unfortunately since hp is not linear with rpm, just getting the plane's engine's rated hp will not be of much help without the engine's power curve.

 

[FactChecker]

The combination of the engine and plane should also be considered. That is called the "installation effects". Installation effects are a combination of the "blockage effect", the "scrubbing drag", and the "compressibility effect" . See Airplane Aerodynamics and Performance by Jan Roskam and C. T. Lan, section 7.5.6 ( https://books.google.com/books?id=b...eller installation affects efficiency&f=false )

 

[etudiant]

JBA's suggestion is clearly an excellent starting point, because it provides a fairly simple way to get directly applicable real world numbers.
While it is possible to get by with much less power in a custom design (Solar Impulse 2 for instance has only 70 hp), the cost of getting a new airframe built is prohibitive.

 

[HowlerMonkey]

Is there a minimum flight speed?

Knowing the speed range of the aircraft as well as specifics on the airframe performance will help you nail down prop shape, diameter, pitch, and power requirements.