Comment on "Ideal Tail Load for Minimum Aircraft Drag"

Abstract

P E. V. Laitone's Engineering Note on ''Ideal Tail Load for Minimum Aircraft Drag, [J. Aircraft 15, 190-192 (1978)] is interesting in its use of the basic biplane equation and Munk's stagger theorem for estimating trim drag. However, there are errors in the conclusions and some of the basic assumptions of the note. First, in modern high-speed transport aircraft the contribution of compressibility drag to the total trim drag problem is very significant. The download on the tail increases the total lift that the wing must carry and if the airplane is operating near the Mach number for drag divergence the required increase of wing angle of attack will cause an increase in compressibility drag. This compressibility contribution is of the order of half of the total trim drag. On the other hand, when compressibility drag is not present the interference term in the biplane equation introduces a negative drag term which compensates to a large degree for the obvious induced drag penalties on the tail due to its download and on the wing due to the greater wing lift. Second, even with compressibility drag, trim drag is generally much less than the 5% mentioned by Professor Laitone. Figure 1 shows the variation of trim drag with center-of-gravity position for various lift coefficients and Mach numbers for a DC-8-54 aircraft. Typically, the DC-8 flies at a CL of about .35. At the original design cruise Mach number of 0.82 and at an average center-of-gravity position of about 26% of the mean aerodynamic chord, the trim drag is 2.2% of the total drag. With some consideration of aft loading cargo the average center of gravity might be moved to about 29%. The trim drag will then be 1.6%. Since the dramatic rise in fuel prices, cruise Mach number has been reduced to 0.8 to reduce compressibility drag. The trim drag penalties are then 1.4% at 26% center-of-gravity position and 0.9% at 29% e.g. position. These representative numbers are well below 5%. Only at high CL and Mach number and at far forward center-of-gravity positions can trim drag approach such high values. Third, Professor Laitone concludes that large trim drag savings could occur if only transport aircraft were designed with larger tails. An aircraft design is a matter of complete integration and a savings in trim drag would have to be weighed against the weight and parasite drag penalty of the larger tail. If we accept the possibility of a 1% decrease in induced drag from the zero tail load case with tail upload this corresponds to something like a 0.4% reduction in total drag since induced drag is approximately 0.4 of the total drag in cruise. Then the total trim drag gain from current practice is of the order of 2.0% of total drag. To gain this 2.0% one would have to move the center of gravity well aft and to do that would require significant increases in the horizontal tail size. Since the horizontal tail contributes about 8% of the total parasite drag or about 4.8% of the total drag it can be seen that a significant increase in this tail size would quickly