# Best margin above a take-off obstacle

#### Jean Claude

##### Junior Member
Ferràn,
I simulated with good accuracy, the standard takeoff of an ELA07 (100 hp) pre-launched at 260 rpm, with the stick fully drawn, ie hub at + 18 °, then balanced on the main gear,
Assumed conditions: Mass 450 kg, Initial propeller thrust 2000 N, Parasite drag : 0.7 m2, Rolling coef. on grass 4%, Ground effect for Z / R = 0.6 True rotor inertia 170 kg m2 or imaginary 120 kg m2 , Aerod. pitch setting 2.8 degrees:

With the rotor inertia of 120 kg m2, instead 170 kg m2, the distance is shorter of 40 meters and the take-off speed little lower.
This shows:
Difference energy of the prop. thrust = 1900 N (average)* 40 meters = 76 kJ
Difference in rolling energy = 2250 N (average) * 4% * 40 meters = 3.6 kJ
Difference on forward speed energy = 0.5 * 450 Kg * (22.2^2 - 20.8^2) = 13.5 kJ

Thus, energy of forward speed gived to the rotor during the take-off run is 76 - 3.6 - 13.5 = 58.9 kJ
while rotor energy difference = 0.5 * (170-120) * (36.6)^2 = 33.5 kJ

It suggests an average "pneumatic efficience" of 0.57

#### Philbennett

##### Junior Member
Can you simulate the optimum hub position?

#### Jean Claude

##### Junior Member
Phil,
I did not seek the optimum. I entered the X and Z positions of the hub and main wheels relative to G and that of the thrust line of the propeller. When the sum of moments around the main whells becomes positive, I enter line by line (every 0.2 s) the angle of the hub to maintain it zero. To be honest, it's a tedious juggling between the rotor spreadsheet (which gives the lift, drag and extra torque as a function of the angle and speed forward) and that of the gyro (which calculates the rpm reached, the forward acceleration, the speed reached and the moment on the main wheels). Automatic correction of the propeller thrust and parasitic drag with the speed forward, correction of the rolling drag with the lightening of the wheels on the ground.
The rotor spreadsheet also takes into account the ground effect according to the forward speed (not negligible)

The results agree very well with the take-off distances and forward speed of the Cierva C30 precisely measured by the Aeronautical Research Committee, under various conditions of pre-launch and load (Report n°1859 )

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#### ferranrosello

##### Member
Thank you very much, Jean C. It is a great job. I don´t know how you are calculating everything, however the results seem to be realistic.
Ferràn