I`m currently working on my thesis in the field of active car aerodynamics. In order to design a controller to move parts of the cars body I need to know how fast the drag and downforce acting on this surface build up. So far I have found out about the Wagner formula, which gives the time dependency as an exponential function dependent on the relative air speed and half chord length (for an aerodynamic profile). This equation, however, results in times as long as a few seconds for maximum force build up. Is that right? I think this process should be way faster.


The car basically has a similar setup as the Pagani Huayra, which has four flaps, that can be moved from 0° to 90°. I have tested a transfer function in Simulink with a velocity of v=80km/h and a semi chord length of b=0.15m, this seems to be close to the dimensions of the Huayras flaps. This gives me a nondimensional time tau=v*t/b=148.148148148*t. The input of the model is a step, which changes the angle of attack to 90° (for example). When I review the simulation result, the force reaches about 99% of the static value after about 0.4 seconds. Is that realsitic? Obviously the cars velocity doesnt reach the speed of a plane, but I expected a faster reaction, especially for critical driving situations where theres not so much time to generate a force in order to stabilize the car. Thank you very much for the help.

  • $\begingroup$ "It depends." On a LOT of things. Do you have a particular set of conditions in mind where your result seems wrong & you'd like a sanity check? Otherwise, this question is likely to be closed as overly broad. $\endgroup$
    – Ralph J
    Commented Nov 30, 2018 at 13:01
  • $\begingroup$ Hi Ralph, thank you for your reply. I have added details in the quation as I cant post a comment that long. $\endgroup$
    – F.Prior
    Commented Nov 30, 2018 at 13:45
  • 1
    $\begingroup$ This question is about unsteady aerodynamics. You should look up Wagner's, Küssner's, and Theodorsen's functions. They might give you different time constants. But I'd check out all three of them. $\endgroup$
    – jjack
    Commented Nov 30, 2018 at 14:17
  • $\begingroup$ This is about it's physics, not aviation. $\endgroup$
    – bogl
    Commented Nov 30, 2018 at 15:52

1 Answer 1


Air is compressable, like a spring, so a slight delay would be reasonable. However, we also have to consider how long it takes to deflect the flap. 0.4 seconds to 99% is not a lot of time, and there would be some effect before that. Electric, hydraulic, and pneumatic may give different deflection rates. Electric may be the fastest. Also, are the flaps automatically deployed by a sensor, or by the driver? There may be a delay there as well. 80km/hour is flying speed for some aircraft. I would try higher and lower speeds as well.

  • $\begingroup$ This seems like a list of suggestions rather than an answer... $\endgroup$ Commented Dec 3, 2018 at 3:49

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