Hover power calculation formula?
 

Purchased the text Helicopter Theory by Wayne Johnson expecting to find a formula for calculating the power required for hover.
The book suggests several different methods to use: momentum theory, blade element theory, force balance method, energy balance method or digital computer.This book is over 1000 pages, yet does not list the units needed to make use of the math formulas. I am stuck.
Can someone give me a simple formula for hover power?
Also please list the units and a sample calculation.
Thanks

Hover program
 

slowrotor.

If you send an e-mail to [email protected], I'll reply and attach a simple hover.exe dos program, by 1996 Erwin Moedersheim. Also attached will be the related .cpp file, so that you can read the C-code.
_______________

Later, if desired, you can send me the necessary inputs. I'll run them through Prouty's 'Combined Momentum and Blade Element Theory for Hover'. This will probably involve a number of back and forth iterations as you modify your parameters.
This is a list of the Inputs Please don't submit the actual form.
This is a tipical output for an Ultralight helicopter

Hover power calcs
 

Slowrotor . Rough rule of thumb to get you going.Every ten pounds you want to lift will require one horsepower.

Dave,
Thanks for suggesting the computer program, unfortunately it wont work on my mac. I could compare your numbers by entering the Mosquito ultralight specs into the X-plane simulator.

Bugdevheli,
You are correct for the typical disc loading.
I am experimenting with very low disc loading that according to my X-plane program can lift 25 lb/hp.
I would like to confirm the X-plane accuracy before I get to far along.

If there was a simple formula that worked to calculate power required to hover, all of us in the flight test business would be out of work!

An approximation can be found in "Helicopter Performance, Stability and Control" by Prouty, but you will still have to wade through the text.

I couldn't work out how to insert mathematical symbols in my reply to this forum. Send me an email and I'll gladly respond with the best approximate formula that I know of for power required to hover

[email protected]

Slowrotor,

The problem is much more than just disk loading, which is easy enough to insert into a momentum formula. see this page for a nice summary:

http://www.eng.upm.edu.my/~aao/week2/week2.htm

The typical total helicopter system figure of merit is about .60 or so (a good rotor alone is about .75 to .80 , but the transmission losses and tail rotor lower that figure). This means for 25 lbs/HP you must have about 1 lb/ft2 disk loading.

For this, you must be able to make a strong stable blade that can be this thin. Example, if you want the whole shebang to weigh 250 lbs less pilot, and then accomodate a 160 lb pilot, you need to have a 410 square foot disk, which requires blades 11.5 feet long. The blades might need to weigh about 10% of the empty weight, so they can only weigh a total of 25 lbs, so you must come up (for a two bladed system) with a pair of blades, each of which weighs 12 pounds and can hold about 420 lbs (for a 2 G max structural capability).
The actual challenge is structural, since this thin, high aspect blade must be stable and strong.

to Mike Hardy and Nick Lappos,
Thanks for quick reply, I might get addicted to this forum.

Nick,
The data I get from X-Plane appears to match with "poor rotor" on the chart you posted above. That means the data from X-plane is conservative.

Why do the rotor blades need to be light?
I saw a picture of a Djinn helicopter that was airfreighted to the Oshkosh airshow last week. The caption said the blades were so heavy the HV envelope was almost nonexistant. Is'nt that good?

slowrotor

p.s. the Djinn compressed air tip jet helicopter photo was on the aero news website last week
www.aeronews.net
edit note: the momentum formula used in this posting does not include rotor profile drag. So X-plane may closer than I thought.

Some technocrats may disagree; but for the best Figure of Merit, the specifications are:

A single blade rotor.
A solidity ratio of 1.0
A NACA 0100 airfoil.

Picture

Dave,
Thats exactly what I am looking for: precise vertical control vehicle.
Could use a bit more forward speed.

slowrotor,

I mention the weight because you must have a tight weight budget to maintain a disk loading of 1.0 Put all the weight you want to into your blades, but then you have to put more into the head to restrain the CF, and then the shaft to support the whole thing, etc.

As an example, the Djinn you mention had very very heavy blades because they had to withstand the tip thrust. The aircraft had a 240 Horse Power engine, so it lifted about 7 lb/hp, about four times worse than the aircraft you envision. Its disk loading was 1.7, even with those strong blades.

I suggest that you start a weight breakdown of the machine, and assign some numbers, then compare to that of other machines, using parametrics (lbs/hp, etc.) to try to put some credibility to your numbers.

The most supreme difficulty in ultra lights and man powered aircraft is to achieve adequate strength/safety while maintaining weight discipline. This is especially true of a whirling blade that must prevent aeroelastic instability while operating in a wide rpm band. Most successful solutions use more engine power, lower radius and higher disk loading because then the structural problems are more easily met.

None of this is an attempt to damp your enthusiasm, good luck!

Nick,
Your comments about ultralight helicopter design are very,very interesting. I hope to hear more.
It's obvious to all that very few, if any, ultralight helicopters have been a success. Often unproven designs are sold to enthusiastic non-aviators that eventually discover they made a big mistake, if they survive.

My assessment of current ultralight designs is that they try to extract more power than the available engines were designed to deliver on a continuous basis. Until affordable high power to weight ratio engines are available wouldn't it make sense to design the helicopter to fly with less power?

Nick wrote "Most successful solutions use more engine
power, lower radius and higher disk loading because then the structural
problems are more easily met."

When the engine fails with a low time sport pilot at the controls, does your higher disc loading recomendation still apply?
I am still trying to comprehend your argument that higher power loading is an advantage. It seems to me that an airframe that can lift 25 lb/hp could include more structure and other safety features than an airframe that lifts 7 lb/hp.

I own a G109 motorglider that can lift 1830 lb with 80hp (23 lb/hp). The large span makes the aircraft heavier, but overall it is more efficient than other airplanes at slow speed and can be flown quietly at low power. It seems to me that a large helicopter rotor would be better for less skilled pilots.

Nick, maybe your point was that designing to meet the 254 lb ultralight weight limit is extremely difficult. I agree.
If a safe sport copter needs to weigh more than 254lb thats fine with me, it can go into the experimental category.
Someone said (I think it was Robborider) that my design goals were contradictory, he may be right.
Keep sending facts and opinions, only the laws of physics can slow my enthusiasm.

slowrotor,

If low disk loading is your primary concern, the optimal configuration is side by side.

This might offer an idea or two

Dave,
I inserted the specification data for the Mosquito ultralight into my X-Plane simulator that uses blade element analysis.
The data output for the Mosquito at 550 lb is:
Hover power 40.7 hp at blade pitch 13.2 degrees.

At 450 lb gross weight the hover power is 31.7 hp at blade pitch 11.3 degrees.

Cruising at 55kt requires 15 degrees pitch and it easily rolls out of control to the left. I assume that is retreating blade stall as lowering the pitch helps for recovery.

If this data is accurate, I believe operating the Mosquito near gross weight could be hazardous.
The Mosquito flies very nice at 450 lb on the simulator so keep in mind the actual aircraft may fly very well. I dont know, but feel I should alert others to the possibility of a problem.

Slowrotor, you should consider getting yourself a good CAD program. You can asign weights, design the parts ect.....
Makes figuring out CG, max TO alot easier.

slowrotor,

I don't know what airfoil(s) the X-Plane simulator uses but the following may be of interest.

The Mosquito's blades appear to be an 8-H-12, and these perform better than the NACA 0012.

At collective pitch of 13.2 and using a NACA 012 blade, Prouty's calculations show 48 HP and 758 lbs of lift.
Regarding Prouty's calculations, the following should be considered;
They were developed for much larger helicopters and may not scale down perfectly.
They are the bare HP for hover at ISA i.e. Sea level, 59 deg F.

Just an additional bit of information
 

Slowrotor,

If you are still interested in optimizing the power to weight ratio, you might find the last paragraph on page 9 and the next paragraph on page 10 of interest.

Study of Dual-Rotor Interference and Ground Effect Using a Free-Vortex Wake Model