1. DRDC-STR 7 8.75 23 -30 to +30 + Series-58 M4621 3 7.34 11.7 -18 to +18 □
2. SUBBOFF 9 8.38 14 -18 to +18 Ellipsoid 12 6.00 4.2 -3to +33 Akron 5 5.91 17 -3to +20 *
3. Munk first introduced force estimation methods in 1922 when he developed a theory for estimating the pitching moment acting on airship hulls at incidence23-26. This theoryis closelyrelated to the slenderbodyapproximation of potential flow theory and is still the basis of many estimation methods in use today. Its major simplifying assumptions include: the radius of the body is much smaller than its length and the angle of incidence is small enough for separation to be negligible. A rigorous development of slender body theory can be found in Karamcheti27,forwhich anadditionalkeyassumption isthattherateofchangeofbodyradiuswith axialdistanceis small. Allen and Perkins28-30realized that all potential flow based force estimation methods assume a pressure recovery on the leeside of the body that does not occur in reality because viscous effects cause flow separation. Allen modeled viscous effects on the normal force distribution by adding an empirical correction to Munk's potential normal force distribution30. In doing so he assumed that viscous effects result in separation that is similar to thatobservedforacylinderin steadycrossflow.
4. /l 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -0.03 Surfacepressureand shear stressbased Vorticitybased, Eq. (14) Munk's potentialtheory