From: William Miller <cwfmd@yahoo.com>
Subject: googlePerf or "cubic gets big", buy less S, not FF
To: lml@lancaironline.net
Date: Monday, December 27, 2010, 10:53 AM

Following up on the perf comparison idea, here's a handy tool, discovered on Google Calculator, for all of us who prefer not to drag out the Mathematica or Matlab, just to do unit conversion. Based on the power formula and conservation of Energy(rate) the formula for level steady state cruise perf is: F=1/2 rho V^2 S    and     Power=F*V =HP     1/2 rho V^3 S = HP = Fuel Flow(FF) * 13.7 HP/(gal/hr)  thanks Jeff for the conversion factor. LOP <65% Substitute this mess into Google calculator, just like a search I backed out S for N330FF to .3185m^2, unfortunately S will vary with Gross weight, because it incorporates induced drag                   S                 V                rho                                   FF input => 0.3185m^2*((187 kts)^3* 1.225 kg m^-3/(2))  /(17gal/hr*13.7hp/(gal/hr)   (0.3185 (m^2) * ((((187 kts)^3) * (1.22500 (kg (m^(-3))))) / 2)) / (((17 (gal / hr)) * (13.7 hp)) / (gal / hr)) = 1.0000512 ignore the round off error, this is back of the napkin okay? input =>m^2*(( kts)^3* 1.225 kg m^-3/(2))  /(gal/hr*13.7hp/(gal/hr)   ((m^2) * (((kts^3) * (1.22500 (kg (m^(-3))))) / 2)) / (((gal / hr) * (13.7 hp)) / (gal / hr)) = 8.16275764 × 10-6 lets call 8.1627e-6 the dimensionless conversion factor  S V^3 =8.1627e-6 FF  with dimensions  S[m^2]  V [kts IAS]  FF(galUS/hr) now you can relate any two input variables to the third And also remind us why there is no free lunch, becuz             FF : V^3 Disclaimer: yes IAS not= CAS EAS etc. This is a linear formula and everybody knows the drag curve is not a straight line.... there are many improvements ahead, but this is fun for front side, steady state, cruise perf. How much did you lower your S by replacing that P-51 scoop with a NACA intake? One last math trick: Divide the junk behind the decimal point by 3 to get the approximate cube root. How much more power required to go 10% faster?  1.1^3 = 1.331 or 33.1% more pwr.