HUMAN POWERED HELICOPTERS

Preliminary Design Considerations

Assumptions

1. Assume maximum available power 0.3 hp
2. Assume total weight (pilot +helicopter) = 250 lb
3. Assume C_L is fixed (since v_o = 0, θ = constant = 0) → α is fixed; C_L = function of α
4. Neglect effect of drag on thrust (C_D/C_L is much less than 1 typically)
5. Assume chord length c fixed
6. Assume r_h = 0

Ω = rotational rate

r_o = blade length

c = chord length

u(r) - air velocity at radius r

r = radial coord

ρ = air density

C_L = lift coefficient

dL = differential lift

L = lift due to one rotor blade

Note, this rough result indicates that thrust on a helicopter rotor

1. Increases quadratically with rotation rate, Ω.
2. Increases cubically with rotor length , r_o.
3. Increases linearly with rotor chord length, c.

Torque Calculation

Using the equation in the propeller theory section we obtain

Given T, the total power Ω QD to rotate the blade is

Let’s now redo the previous calculation, assume available power equals 500W, Ω = 2π rad/s, c = 0.1m, ρ = 1kg/m³, C_L = 1.0, C_D = 0.1 (see figures attached to propeller theory section). What is the available thrust?

Let’s do the calculation once more by specifying P and F_T (= total weight) and solving for r_o and Ω. C_L, C_D, ρ will be assumed fixed and equal to 1, 0.1 m, 0.1 and 1kg/m³ respectively.

Assume P = 400W (a bit more realistic)

2^nd attempt – solve for r_o and Ω in terms of other parameters. Also, assume N propellers

Noting that

If we specify a seemingly slow rotation rate of 1 rad/s (= Ω), then cN ≈ 25m. Using this in equation (2a), we obtain r_o = 8m, which seems reasonable, in order to achieve a total chord length cN ≈ 25m, we could specify 25 propellors, each having a chord length of 1m, 50 propellers having 0.5m chords, 100 propellers having 0.25m chords, etc.

Moral: Designing a human powered helicopter will be fairly difficult, but apparently doable.