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I am theorizing a drone helicopter from a tesla powertrain (P100D). Lets assume the system is theoretically maximized with an optimum propeller (this is what I am currently stuck on). How much thrust could a Tesla powertrain produce (I understand the thrust would decrease as the battery drains and voltage decreases, just wanting to get an idea of theoretical optimal thrust)?

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    $\begingroup$ Try something. Put your car's accelerator pedal to the floor and hold it there continuously for an hour. You can't. Within 10 seconds, safe operation will oblige you to abort the experiment. Car engine design absolutely relies on that; they're like a starter motor, good for 5 seconds but absolutely not made to run that power continuously. Your "200hp" engine might be good for 30hp continuous. Tesla's powertrains will have the same constraint, the motor isn't sized for continuous at-rating operation. $\endgroup$ – Harper Nov 7 '17 at 7:39
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For a propeller/rotor, net consumed power = torque * rpm. For an electric drivetrain, net power delivered = current * voltage, with current equating to torque and voltage to rpm. Tesla should have really good data analyses on the power delivery as a function of demand over time, with wheel torque and wheel rpm as parameters.

Then you only have to replace the propellant medium: slippery air instead of the stony fixed world. Torque is a measure of drag of the rotor blade, thrust is a measure of lift. Both are a function of rpm as well, usually the rpm is limited by the tip speed approaching the speed os sound and is chosen to be as close as possible to it.

So a design process might be:

  1. Determine payload.
  2. Determine approximate disk load by comparing with existing designs, resulting in the disk area and the blade radius.
  3. Compute rpm so that tip speed is about Mach 0.8
  4. Compute power, torque and thrust from data available for comparable comfigurations.

Two books that contain chapters on pre-design of helicopters are Helicopter Performance, Stability and Control by Raymond Prouty, and Helicopter Aerodynamics by J. Gordon Leishman.

But the area that will give you most headache won't be computing the thrust etc, it will be figuring out how to control the flight path. Do you plan to use a swash plate?

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