Mass of fuel is an important criterion ignoring the

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mass of fuel is an important criterion. Ignoring the climb to and descent from cruise altitude, and assuming that all aircraft and engine characteristics except total mass are constant throughout cruise, one can easily obtain an estimate of range.
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ENGINE PERFORMANCE PARAMETERS In level flight at constant speed, engine thrust and vehicle drag are equal, as are lift and vehicle weight. Therefore T= D=L(D/L)=(mg)/(L/D) where m is the instantaneous vehicle mass, g is the acceleration due to gravity, D is drag force, and L/D is the lift-drag ratio. The thrust power is then Tu=mgu/L/D
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ENGINE PERFORMANCE PARAMETERS As we know that η o th η p = Tu/ṁ f Q R Using above equation with this expression of thrust power, we obtain f = mgu/ η o Q R (L/D) However, since the fuel is part of the total aircraft mass m, f =-dm/dt or f =-udm/ds Where s denotes distance along the flight path.
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ENGINE PERFORMANCE PARAMETERS Then considering above two equations we can write dm/ds=-mg/ η o Q R (L/D) If, as an approximation, the denominator is assumed constant, the range s of the vehicle can be obtained by integrating above equation to obtain Brequet’s rage formula, s= η o (L/D)ln(m 1 /m 2 ) Q R /g Where m 1 and m 2 are initial and final masses of the vehicle, the difference being the mass of the fuel consumed. Thus the range is directly proportional to the overall efficiency η o . As the overall efficiency is η o = (u e -u)u /f Q R and that for given u e , η o is maximum for u= u e /2.
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ENGINE PERFORMANCE PARAMETERS Overall efficiency can be modified for the engine of double propellant streams. It is only necessary to replace the exhaust velocity by the “ thrust-averaged ” exhaust velocity ȗ e which is defined as ȗ e = ṁ aH (1+f)u eH +ṁ aC u eC )/ ṁ aH (1+f)+ ṁ aC and to replace the fuel- air ratio f by the term f/1+ (ṁ aC / ṁ aH ), thus η o = [1+ (ṁ aC / ṁ aH )](ȗ e -u)u/fQ R For given ratio aC / ṁ aH
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