Quest for Performance: The Evolution of Modern Aircraft



Appendix C

Estimated Aerodynamic Parameters



[509] Appendix C presents the methods employed for estimating the aerodynamic parameters given in tables I to IV in appendix A. The parameters were estimated from published performance data for the various aircraft. In most cases, the performance data in the tables formed the basis for the calculations. The methods are briefly described in the following paragraphs.


The zero-lift drag coefficient was determined from the equation


equation for the zero lift drag coefficient(C1)




zero-lift drag coefficient


total drag coefficient for given combination of power, speed, and altitude


induced drag coefficient corresponding to same flight conditions as total drag coefficient



The total drag coefficient can be estimated from the following relationship:


equation to determine the total drag coefficient(C2)



semispan wing position

propulsive efficiency


engine power, horsepower

atmospheric density at sea

sea-level density, slugs per cubic foot

atmospheric density ratio

atmospheric density ratio for some altitude other than sea level

S [510]

wing area, square feet


speed, statute miles per hour



Equation (C2) can be put in the form


Equation used for estimating the value of the drag coefficient(C3)


by substituting a value of 0.002378 for the standard atmospheric density at sea level. Equation (C3) was used for estimating the value of the drag coefficient CD. The values of propulsive efficiency semispan wing positionemployed in equation (C3) varied between 0.70 and 0.85, depending on the aircraft, and were chosen on the basis of information contained in references 95 and 120.

The induced drag coefficient CD, i was obtained from


formula for induced drag coefficient




lift coefficient formula


which can be combined to give


induced drag coefficient formula(C4)





weight, pounds


wing loading, pounds per square foot

airplane efficiency factor

airplane efficiency factor


aspect ratio, K2 b/2/S


wing span (upper wing span for biplanes and triplanes), feet


wing area (includes all wings for biplanes and triplanes), square feet


Munk's span factor (for biplanes and triplanes)



[511] Munk's span factor is a function of the geometry of the multiplane wing arrangement and can be either less or greater than 1.0. On the basis of information given in references 46 and 103, an average value of the span factor of 1.1 was used for all biplane configurations, and values of K of 1.22 and 1.16, respectively, were used in computing the aspect ratios of the Fokker and Caproni triplanes discussed in chapter 2. Values of the airplane efficiency factor in the range of 0.70 to 0.75 were used, with the exact value dictated by the configuration and refinement of the aircraft.


The value of the maximum lift-drag ratio (L/D)max was computed by equation (3.20) given in chapter 3 of reference 90 as


Maximum lift drag ratio formula(C5)


In addition to the assumptions described in the preceding paragraphs, the accuracy of the calculated aerodynamic parameters depends on two other important assumptions. First, the accuracy of the calculated results obviously depends upon the accuracy of the published information on the various aircraft; and, second, the accuracy depends on the completeness of the performance information. For example, can the power be determined for a given combination of speed and altitude. No general assessment of either of these possible sources of error can be made. Aerodynamic parameters for those cases in which the performance data were incomplete or could not be estimated with reasonable confidence were not included in the tables; and if comparative performance data for different aircraft showed unexplained anomalies, aerodynamic data were not presented for the aircraft whose published performance characteristics seemed questionable.