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I am doing some calculations for preliminary design of an airplane and I was wondering how I would go about determining the minimum thrust to weight ratio needed for the aircraft to takeoff. Which factors play a role and how are they limiting the thrust to weight ratio?

I admit the question is vague but it is intended to be that way. My team and I are tasked with building a Distributed Electric Propulsion based aircraft and the only other requisite apart from it being fully electric is that it must have a wingspan of at least 3 ft. Everything else is completely up to us to estimate and design.

I am looking for guidance on what factors I have to consider or what mathematical methods I would have to employ in order to estimate a necessary Thrust/Weight ratio

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    $\begingroup$ It depends how long your runway is... $\endgroup$ – Michael Hall Mar 3 at 4:26
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    $\begingroup$ @Michael Hall: And the airfoil used for your wings, and how much drag your fuselage &c has. $\endgroup$ – jamesqf Mar 3 at 5:02
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    $\begingroup$ Start with 0.3 and check against your take off run, top speed and climb requirements. Clearly, a glider-like airplane can fly with less thrust/weight than a supersonic fighter. $\endgroup$ – Peter Kämpf Mar 3 at 6:30
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    $\begingroup$ Honestly, it looks like you haven't done any. What do you expect us to do? Safe rate of climb is a good place to start, lest you spend lots of time following early Wright Brothers research. Plenty of power is available these days, particularly with electric motors. $\endgroup$ – Robert DiGiovanni Mar 3 at 12:11
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    $\begingroup$ A little information on what you are designing would help. $\endgroup$ – Robert DiGiovanni Mar 3 at 12:18
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Without knowing more about what you are designing it is impossible to come up with a specific number.

But there are a number of factors that you should take into account:

  • the lower the thrust to weight ratio, the longer it will take to accelerate, so the longer the required runway will be. During the take-off roll the lift can usually be neglected, but the parasitic drag and roll drag will increase with speed. The faster you go, the slower you accelerate. You need to have enough thrust to achieve your take-off speed within a reasonable distance.

  • at take-off, the thrust still needs to exceed the drag, otherwise you will have no excess power available to climb.

  • after take-off, you typically need to achieve a certain rate of climb and a certain climb angle to clear obstacles. This is affected by the thrust to weight ratio. If you require a climb angle of 10°, you need a thrust to weight ratio of $\sin(10°) \approx 0.17$ just for the climb, even if you have no drag. With a lift to drag ratio of 8 at take-off conditions, you would end up at a thrust to drag ratio of at least. $\frac{D}{L}+sin(\gamma) = \frac{1}{8}+sin(10° )\approx 0.3$

  • you may want to achieve a certain top speed with the aircraft. Check what the thrust to weight ratio is required in those conditions. It may be higher than what is needed for take-off.

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