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I'm working on a project which requires me to determine the power requirements of a propulsion system from a specific take-off distance. Starting with this equation: $$ s_g\approx \frac{1.21(W/S)}{g\rho (Cl)_{max}(T/W)} $$ I rearranged to get $$ T=\frac{1.21(W^2/S)}{g\rho Cl_{max}s_g} $$ My question is: Is this the total thrust at takeoff, and if so, is this (following equation) a valid method of determining the power requirements? $$ P_{req}=\frac{TV_{lo}}{\eta _{prop}} $$

Thanks in advance!

Abu Sinan
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  • How did you get that equation? – sophit Mar 16 '23 at 15:17
  • @sophit I took it from the textbook "Aircraft Performance and Design" by John D. Anderson – Abu Sinan Mar 16 '23 at 15:50
  • There's no explanation about how to use it in the book? – sophit Mar 16 '23 at 16:05
  • @sophit returning back to the textbook it mentions that T/W in the original equation is evaluated at a velocity of 0.7Vlo (average T/W using average velocity), does this mean its not valid to use the actual lift-off speed? I would like to figure out the absolute max thrust and power required throughout the takeoff and climb – Abu Sinan Mar 16 '23 at 16:25
  • "quick & dirty" equations like that one normally refer to "nominal" conditions: T is the max thrust available @ all engines operative, W it max takeoff weight and S the nominal wing surface. You plug everything inside and you get the field length or the needed T/W to stay under a certain length. This answer should also help you. – sophit Mar 16 '23 at 16:52
  • @sophit perfect! thank you very much – Abu Sinan Mar 16 '23 at 17:09
  • You're welcome – sophit Mar 16 '23 at 21:21

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