## Help Design a Human-Powered Helicopter

 Quote by Cyrus With no calculations to show the power requirements, or the estimated weight, this is really unsupported speculation. I would avoid such statements with nothing to back it up. His idea sounds absolutely terrible.
Do you have any idea how to calculate the lift from one of these laminar air devices; I have no idea how to approach it?

 Quote by Phrak 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.

 Quote by Cyrus 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.

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.
Attached Files
 human powered helicopter (updated).xls (29.5 KB, 18 views)

 Quote by Brian_C 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, dont even think about it).

Recognitions:
 Quote by Phrak 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.

 Let's just forget this thread ever happened.

 Quote by FredGarvin 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?

 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?)
 Blog Entries: 1 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 accomodate the pilot's additional weight gain. Thus, the new total weight of airframe and powerplant would be 3,050.7 lbs.

 Quote by Phrak 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 dont 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.

 Quote by 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.)
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 accomodate 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.

 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.

 Quote by 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, ...
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.

 Quote by Phrak 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.

 Quote by 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 accomodate 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.

$$M = k V^2 L^3$$

 Quote by Phrak I would initially presume that HP/Mass_of_pilot is constant.
 Quote by Cyrus 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.