Help Design a Human-Powered Helicopter

[Cyrus]

Do you have any idea how to calculate the lift from one of these things; I have no idea how to approach it?

No clue - and that's what worries me. If you find anything let me know because I'd be really interested to see how. These things are pretty much the 'magic crystals' and 'healing pyramids' of aerospace, IMO.

 

[Phrak]

No clue - and that's what worries me. If you find anything let me know because I'd be really interested to see how. These things are pretty much the 'magic crystals' and 'healing pyramids' of aerospace, IMO.

I've been scrolling around YouTube for one of the toy demos I once ran into, and can't find one anymore. Apparently I don't know the keywords to use.

 

[Brian_C]

I made an algebraic error. Can you tell I'm not a helicopter engineer? See attached.

I think you would need to perform an iterative calculation to come up with realistic results. For a given body weight of the operator, you have to calculate the minimum rotor diameter, then update the total weight of the operator/vehicle based on the added weight of the rotors. When you plug the updated weight (thrust) into the momentum equations, you end up with an even larger rotor diameter! The results will probably not converge unless you use a super light-weight material.

 

[Cyrus]

I made an algebraic error. Can you tell I'm not a helicopter engineer? See attached.

I can't seem to open this MATLAB file.

You should never present your results in units of acres, but otherwise the diameter is now correct. You are pardoned of your engineering sin... this time.

Edit to your edit: To go to the next level analysis, you need to write a BEMT code. Here you can account for prandtl tip losses, lift/drag for your chosen airfoil section, pitching moments, and ground effect. This is not pretty, and should not be attempted in excel (seriously, don't even think about it).

 

[FredGarvin]

I think your .002 value of air density may be off, but I've only visited one web site.

That is the standard day air density converted to sl/ft^3. It's right.

 

[Brian_C]

Let's just forget this thread ever happened.

 

[dr dodge]

a badger? did I hear a badger?

dinsdale?

dr

 

[Phrak]

That is the standard day air density converted to sl/ft^3. It's right.

OK. I get .00237 slug/ft^2 for international standard density at sea level. Interesting that the thrust is the 1/3 power of the density, so that the variation in density is not so critical. On a crisp cold morning in Death Valley one could exptect to get about 8 to 9% better lift over standard day air density.

How is the standard day air density obtained?

 

[Phrak]

Here's one for you, Cyrus. Have you done the scaling analysis on this sort of problem?

If the weight of the pilot is doubled, how does the size of the structure increase to obtain the same material stresses. The question akin to this is to obtain the same bending radiuses based on material rigidity. I'm not sure if this one should be compared against doubling the total mass or doubling a length, or what-have-you.

The last I can think of asking is how aerodynamic forces scale with a doubling in size of the airframe. (Should fluid velocity be kept constant or also double for this?)

 

[mugaliens]

All things being equal, and discounting Reynold's numbers as the weight of the pilot is usually substantially less than than of the airframe and powerplant, whatever the overall weight increase of the pilot increases the total MGTOW, the airframe and powerplant would require a similar increase to achieve the same performance (same stall speed, time to climb, etc.)

Example: Your pilot initially weighs 150 lbs, but after feasting for two years arrives at 300 lbs. His old plane's empty weight + useable fuel was 3,000 lbs.

He has money galore, but loves his old plane, so he's commissioning the design and building of a new plane that'll match the old plane's performance characteristics exactly.

Percentage Increase: (3300-3150)/3150 = 4.8% increase in overall weight of the airframe and powerplant. Because weight increases as the cube of an single dimension, the pilot's new aircraft would have to be just 1.69% larger in any dimensional direction to accommodate the pilot's additional weight gain.

Thus, the new total weight of airframe and powerplant would be 3,050.7 lbs.

 

[Cyrus]

The last I can think of asking is how aerodynamic forces scale with a doubling in size of the airframe. (Should fluid velocity be kept constant or also double for this?)

Aerodynamic forces don't change due to airframe size, they depend on the rotor specifications. The "fluid velocity", is termed the rotor inflow, and be calculated (to first order) using the inflow equation.

 

[Cyrus]

All things being equal, and discounting Reynold's numbers as the weight of the pilot is usually substantially less than than of the airframe and powerplant, whatever the overall weight increase of the pilot increases the total MGTOW, the airframe and powerplant would require a similar increase to achieve the same performance (same stall speed, time to climb, etc.)

The Reynolds number does not change with the weight of the pilot (or weight in general), so I'm not sure where you're going with this. Also, the pilot weight here is substantial >%50 of the vehicle weight, so your analysis is not valid in this application.

Percentage Increase: (3300-3150)/3150 = 4.8% increase in overall weight of the airframe and powerplant. Because weight increases as the cube of an single dimension, the pilot's new aircraft would have to be just 1.69% larger in any dimensional direction to accommodate the pilot's additional weight gain.

Thus, the new total weight of airframe and powerplant would be 3,050.7 lbs.

This scaling rule is good for intial insights, but one can simply use the equation I provided to see exactly how the rotor radius changes in response to changes in vehicle weight.

 

[Phrak]

I'll have to reread your posts tomorrow with better consideratioin, Cyrus. But this is the reason I ask: Of the 186 tour de France entrants in one year, their weight averaged 156 pounds. We might take this as the optimum weight for best cyclists. Human flight requires some more consideration, as I'm sure you know. The mass of the pilot and how this scales the weight of the aircraft becomes a factor.

But as a baseline, after some research, the average, midline, World Class, 156 pound cyclist can deliver 449 Watts = 0.603 HP = 331 ft-lb-sec^-1 over a 5+ minute duration.

I would initially presume that HP/Mass_of_pilot is constant.

 

[Phrak]

All things being equal, and discounting Reynold's numbers as the weight of the pilot is usually substantially less than than of the airframe and powerplant, ...

In this case, such as it is, as Cyrus has said, initially consider the pilot and airframe about equal. Maybe start with an initial estimate of the pilot at 140 lb. and airframe at 30% more, and go from there.

 

[Cyrus]

I would initially presume that HP/Mass_of_pilot is constant.

It decays, but the rate of decay would have to be found experimentally for a particular person.

 

[Phrak]

All things being equal, and discounting Reynold's numbers as the weight of the pilot is usually substantially less than than of the airframe and powerplant, whatever the overall weight increase of the pilot increases the total MGTOW, the airframe and powerplant would require a similar increase to achieve the same performance (same stall speed, time to climb, etc.)

Example: Your pilot initially weighs 150 lbs, but after feasting for two years arrives at 300 lbs. His old plane's empty weight + useable fuel was 3,000 lbs.

He has money galore, but loves his old plane, so he's commissioning the design and building of a new plane that'll match the old plane's performance characteristics exactly.

Percentage Increase: (3300-3150)/3150 = 4.8% increase in overall weight of the airframe and powerplant. Because weight increases as the cube of an single dimension, the pilot's new aircraft would have to be just 1.69% larger in any dimensional direction to accommodate the pilot's additional weight gain.

Thus, the new total weight of airframe and powerplant would be 3,050.7 lbs.

OK. You motivate me to do this thing. The simplest is a rescaling of lengths. I prefer doubling. It makes things easier to consider. If materials density is constant then mass increases as 2³, as you've noted.

However, aerodynamic forces, Lift and Drag will increase by the factor 2², from

L = k V^2 L^2

D = k V^2 L^2

where L is some typical length. (This will assume, the change in typical length doesn't significantely effect Reynolds number, as you've also noted.)

Aerodynamic moments increase as 2³.

M = k V^2 L^3

I would initially presume that HP/Mass_of_pilot is constant.

It decays, but the rate of decay would have to be found experimentally for a particular person.

I'm not sure what you mean, but was saying that I would initially assume that over a population of world class cyclists that cycling power is proportional to the mass of the rider over a realistic weight range of, say 120 to 180 pounds.

 

[mugaliens]

Good catch, Phrak. It's why modern larger jets are more efficient in terms of lb-miles traveled per lb of fuel consumed than modern smaller jets.

Given my computations for a light airplane, it won't amount to much at all.

Given the fact you're desiging for a human-powered helo, however, it'll mean a great deal.

I had an idea: Have you considered using solar concentrators, built into the wings, to gather sunlight, piping it down light-tubes to the center where it's used to power a Stirling engine to sping the prop? Or, in the case of your helo, you could have engines mounted about 2/3 of the way out along the rotors, and smaller props to push the rotors around?

Just a thought. I also thought about putting the cyclists out there, as well, if you want to keep the engines fully human.

 

[Phrak]

Good catch, Phrak. It's why modern larger jets are more efficient in terms of lb-miles traveled per lb of fuel consumed than modern smaller jets.

Really, I'm not sure how this works out. Can you give details?


But there is still stress and strain to consider for human powered flight, in general.

Do you recall something called the Square-Cube rule, or square-cube law as applied to the strength of a bone or beam, or even a wing as it scales in length only? The idea is to keep material density unchanged, and the shapes of everything stay the same. It's just scaled up in size. Latently I found that the amazing Wikipedia provides it.

http://en.wikipedia.org/wiki/Square-cube_law"

For Aerodynamic Forces:

"When a physical object maintains the same density and is scaled up, its mass is increased by the cube of the multiplier while its surface area only increases by the square of said multiplier. This would mean that when the larger version of the object is accelerated at the same rate as the original, more pressure would be exerted on the surface of the larger object."

For the Stength of a Beam:

"If an animal were scaled up by a considerable amount, its muscular strength would be severely reduced since the cross section of its muscles would increase by the square of the scaling factor while their mass would increase by the cube of the scaling factor."

Unfortunately Wikipeda doesn't present this in terms of the yield strength of a cantilivered beam (or wing) (or rotor), but we can replace "muscle strength" by "yield stress".

The strength of the beam increases as L² and the mass increases as L³.

I'm still trying to find how rigidity scales.

I had an idea: Have you considered using solar concentrators, built into the wings, to gather sunlight, piping it down light-tubes to the center where it's used to power a Stirling engine to sping the prop? Or, in the case of your helo, you could have engines mounted about 2/3 of the way out along the rotors, and smaller props to push the rotors around?

The challenge in this thread is human powered flight, but check out the NASA Pathfinder.

http://www.nasa.gov/centers/dryden/news/FactSheets/FS-034-DFRC.html"

Under the hot summer midday sun, you might expect one horse power per square yard of solar insulation. The best Solar electric panels are about 15% efficient, I think...

Just a thought. I also thought about putting the cyclists out there, as well, if you want to keep the engines fully human.

Well, I did too, but no one took me seriously. It would significantly reduce the weight-per-pilot requirement of the airframe--by as much as 50%. But there's a catch. There must be at least one crew member that cannot rotate but face the same direction throughout the flight.

(BTW, very cool stuff you had on the crosswind landing thread.)

 

[Cyrus]

What do you mean by "put the pilot out there." The rules clearly state the pilot cannot be rotating.

 

[Phrak]

What do you mean by "put the pilot out there." The rules clearly state the pilot cannot be rotating.

"Cyclists", in plural, Cyrus. Say you have four blades and put the cyclists in the center of each blade. This means that the bending stress on the blades is cut in half. Belatedly, I recall (to first order, see Poison ratio) that the strain, that leads to coning, is also cut in half.

The rules state that at least one member of the crew must face in the same direction throughout the flight. So this ...complicates things.

How would you go about having at least one nonrotating crew member, where the crew, as the rules call them, are dispersed about the blades to save stuctual weight?

 

[Cyrus]

"Cyclists", in plural, Cyrus. Say you have four blades and put the cyclists in the center of each blade. This means that the bending stress on the blades is cut in half. Belatedly, I recall (to first order, see Poison ratio) that the strain, that leads to coning, is also cut in half.

Did you just throw in a bunch of words together hoping it would make sense? Sorry, no.

The rules state that at least one member of the crew must face in the same direction throughout the flight. So this ...complicates things.

A bit of common sense() shows that the rules were intended to imply that the rotorcraft needs an anti-torque device. You can email the rules committee if you want clarification and post their reply here.

 

[Phrak]

Did you just throw in a bunch of words together hoping it would make sense? Sorry, no.

no, I did not

 

[dr dodge]

dual rotors (internally pressurized for strength) for inertial stability
double cone/roller drive assy.
I am working on sketches for an RC model

dr

 

[Cyrus]

dual rotors (internally pressurized for strength) for inertial stability
double cone/roller drive assy.
I am working on sketches for an RC model

dr

What on Earth does that mean. Internal pressure does not change material properties. And the rotation of the blades will cause all the air to...(think about it).

 

[mugaliens]

Really, I'm not sure how this works out. Can you give details?

It's precisely as you noted: Volume and mass of an aicraft increase as the cube of a scaled length, as does the induced drag. However, their parasitic drag, which is most of the drag while at cruise, increases only as the square of a scaled length.

But there is still stress and strain to consider for human powered flight, in general.

Yes. However, all other factors being equal, you're more likely to be successful if you design it to be powers by eight cyclists than you are if it's designed to be powered by four, due to the cube-square issue, above.

Do you recall something called the Square-Cube rule, or square-cube law as applied to the strength of a bone or beam, or even a wing as it scales in length only? The idea is to keep material density unchanged, and the shapes of everything stay the same. It's just scaled up in size. Latently I found that the amazing Wikipedia provides it.

http://en.wikipedia.org/wiki/Square-cube_law"

For Aerodynamic Forces:

"When a physical object maintains the same density and is scaled up, its mass is increased by the cube of the multiplier while its surface area only increases by the square of said multiplier. This would mean that when the larger version of the object is accelerated at the same rate as the original, more pressure would be exerted on the surface of the larger object."

As this applies to a wing, you're going to have higher wing loading with a scaled up version. This is why we can build scaled models of fighters that required steel and aluminum alloys while we can use balsa and plywood build a scaled R/C version that'll pull 20 Gs.

Under the hot summer midday sun, you might expect one horse power per square yard of solar insulation. The best Solar electric panels are about 15% efficient, I think...

Market leader's SunPower's panels conversion ratio is 19.3%. However, we're concerned less with electrical power output per square foot than we are with power per lb. The current world record is 41.6%, achieved on August 26, 2009. For thin-films, which are much lighter than crystalline, it's expected to range from 30% to more than 35% over the next decade.

Well, I did too, but no one took me seriously. It would significantly reduce the weight-per-pilot requirement of the airframe--by as much as 50%. But there's a catch. There must be at least one crew member that cannot rotate but face the same direction throughout the flight.

Yes, the pilot! Well, he can darn well pedal, too!

(BTW, very cool stuff you had on the crosswind landing thread.)

Thanks!

 

[dr dodge]

Internal pressure does not change material properties. And the rotation of the blades will cause all the air to...(think about it).

pressure does change the properties of a sealed container. take a piece of plastic tubing good to 200 psi. no positive pressure differential, its limp as a ...whatever
put 200 psi positive pressure, you can hold one end and it will stand erect. rocket tanks have no structural rigidity without positive pressure.

and do you think all the air will fly out to the ends?

dr

 

[Cyrus]

pressure does change the properties of a sealed container. take a piece of plastic tubing good to 200 psi. no positive pressure differential, its limp as a ...whatever
put 200 psi positive pressure, you can hold one end and it will stand erect. rocket tanks have no structural rigidity without positive pressure.

and do you think all the air will fly out to the ends?

dr

My point was that it will change the rigidity of the structure, but not its strength. The strength is a material property inherent to the plastic. It will yield at some sigma stress value, air or no air.

As for the air going to the ends. Not "fly out", but it will "pile up" due to pressure gradient. There is going to be a radial acceleration. My friend is doing pneumatic trailing edge flap actuation on rotor blades and has this very problem. The centrifugal force is:

F_{cf}= \frac{M \Omega^2 R}{2}​

 

[dr dodge]

the added rigidity would decrease the structure needed.
obviously it does not change the strength

this then potentially would allow less mass of the rotors.
as far as "pile up", are you saying that the rotation would significantly increase the pressure inside the rotor at the ends?

dr

 

[Cyrus]

the added rigidity would decrease the structure needed.
obviously it does not change the strength

Perhaps, if you could resolve the centrifugal force problem. I suspect you would find the airfoil sections to be 'bulging' near the tips, and under inflated at the root.

this then potentially would allow less mass of the rotors.
as far as "pile up", are you saying that the rotation would significantly increase the pressure inside the rotor at the ends?

dr

It's certainly possible.

 

[mugaliens]

It's certainly possible.

It's reality, and the fundamental basis behind radial-flow compressors.