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Re, Mach dependence

A few comments are in order on the TYPE command, which allows the user to set the dependence of the Mach and Reynolds numbers on CL.
Any CL-CD polar can be of the following three types:

Type parameters held constant varying fixed —- ———————— ——- ———– 1 M , Re .. lift chord, vel. 2 M sqrt(CL) , Re sqrt(CL) .. vel. chord, lift 3 M , Re CL .. chord lift , vel.

  • Type 1 corresponds to a given wing at a fixed velocity going over an angle of attack range, as in a wind tunnel test alpha sweep or a sudden aircraft pullup. This is also the common form for an airfoil polar.

  • Type 2 corresponds to an aircraft in level flight at a given altitude undergoing trim speed changes. This is the most useful airfoil polar form for determining a drag polar for an aircraft at 1-g. For this case, The “Mach number” input with the MACH command is actually interpreted as the product M sqrt(CL), and the “Reynolds number” input with the VISC or RE commands is actually interpreted as RE sqrt(CL). For a wing in level flight, these products can be computed from the following exact relations, with Re based on the mean chord:

                       1/2                                1/2
        |  2  W/S |                     1  | 2 rho W |  M sqrt(CL) = | --- --- |       RE sqrt(CL) = -- | ------- |
        | 1.4  p  |                     mu |    AR   |

W = weight p = ambient pressure S = wing area mu = dynamic viscosity AR = aspect ratio rho = ambient air density

  • Type 3 corresponds to a wing of “rubber chord” with a given lift at a given speed. This is best used for selecting an optimum CL for an airfoil while taking Reynolds number changes into account.
    The product RE CL can be computed from the following:

         2 W RE CL = ------       b = span = sqrt(S*AR)
    mu V b

Caution must be used with Types 2 and 3 so as to not allow the CL to go negative. In addition, with non-zero Mach and Type 2, the CL must not fall below that value which makes Mach exceed unity. Warning messages are printed when these problems occur.