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Assuming a flat bottom wing moving through the air at say 50km/h and at zero degree angle of attack, what will be the likely airspeed above and below the wing?

I know this will be affected by camber and maybe wing chord too. But is there like a proportional estimate for specific wing camber?

I haven't got much knowledge about wing maths, but a formula would be appreciated.

Applying Bernoulli's equation requires the relative airflow above and below the wing. The things is, I'm trying to experiment with the fact that given atmospheric pressure, the two different airflows, and the wing area, one can actually determine the pressure difference between the top and bottom surface using Bernoulli's equation and also the total force holding the plane up by getting the product of the pressure difference and the wing area. So what I'm trying to do is estimate the lift force on my theoretical airplane model at a particular wind speed. I want to use this to estimate the minimum airspeed required for normal flight 'without flaps'.

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  • $\begingroup$ Might be worth also asking this at physics.stackexchange.com to get an in depth answer of fluid dynamics. $\endgroup$
    – Adwaenyth
    Commented Aug 11, 2017 at 14:06
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    $\begingroup$ We would need more information on what the rest of the wing would look like. Apart form the bottom. $\endgroup$
    – Koyovis
    Commented Aug 11, 2017 at 14:28
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    $\begingroup$ There isn't just a single airspeed on top and another airspeed on bottom. Airspeed varies continuously over the top and bottom surfaces; for example see mh-aerotools.de/airfoils/velocitydistributions.htm $\endgroup$
    – David K
    Commented Aug 11, 2017 at 17:26
  • $\begingroup$ That page also shows that an airfoil can be giving a lifting force even though speed of air flow over large parts of both the top and bottom is greater than the speed of the undisturbed airflow. $\endgroup$
    – David K
    Commented Aug 11, 2017 at 17:33
  • $\begingroup$ Angle of attack has a large influence on speed of the air flow over the wing. $\endgroup$
    – David K
    Commented Aug 11, 2017 at 17:34

3 Answers 3

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The short answer is that it is possible, by way of knowing the pressure distribution and applying the Bernoulli equation to relate the pressure and the velocity.

More specifically to your question, I'm not aware of any published correlation between camber and air velocity (nor do I think it'd have much practical application), but you could come up with your own by running a variety of geometries through XFOIL for a given airfoil geometry (maybe a Clark Y of varying camber for a flat-bottomed design) and applying Bernoulli on the calculated pressure distribution for whatever freestream atmospheric conditions and chord length you want.

Another note: You asked specifically about a wing, not an airfoil. A wing will have lots of other effects contributing to variations in velocity over its surface; there is no easy way to account for all of them.

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OK if it is lift that you would like to compute, this is the way it is commonly done:

$$ L = C_L * \frac {1}{2} \cdot \rho \cdot V^2 \cdot A $$

With

  • L= lift [N]
  • $C_L$ a lift coefficient depending on aerofoil shape and angle of attack $\alpha$ [dimensionless]
  • $\rho$ = air density [kg/$m^3$]
  • V = airspeed (of the aircraft) [m/s]
  • A = wing area [$m^2$]

If you would like to use a flat bottomed profile, you could use Clark Y. This image is a bit fuzzy but you could construct a straight line $C_L - \alpha$ from the graph. enter image description hereImage source

At $\alpha$ = 0 the $C_L$ is about 0.4, so at sea level, with an airspeed of 100 m/s and a wing area of 10 $m^2$ the lift would be:

$$ L = 0.4 \cdot \frac {1}{2} * 1.225 * 100^2 * 10 $$

= 24,500 N. So the pressure differential over the wing area is 2,450 N/m$^2$ If this would be from increased dynamic pressure over the wing only, the air speed on top of the wing would be:

$$ 2,450 = \frac {1}{2} \cdot \rho \cdot (V_{top}^2 - V_{bottom}^2) => V_{top} = \sqrt{\frac{2,450 \cdot 2 }{ 1.225} + 100^2} = 118.3 m/s$$

In that particular case, at angle of attack zero, with no skin friction or boundary layer, static pressure underneath the wing equal to atmospheric pressure etc etc, the speed under the flat wing surface would be the airspeed = 100 m/s and over the wing would be 163.2 m/s. But the creation of aerodynamic lift is way more complicated than only considering the speeds over and under a wing section and assuming that lower surface pressure = atmospheric pressure, that is why it is done with the $C_L - C_D$ graphs.

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Applying Bernoulli's equation requires the relative airflow above and below the wing. The things is, I'm trying to experiment with the fact that given atmospheric pressure, the two different airflows, and the wing area, one can actually determine the pressure difference between the top and bottom surface using Bernoulli's equation and also the total force holding the plane up by getting the product of the pressure difference and the wing area. So what I'm trying to do is estimate the lift force on my theoretical airplane model at a particular wind speed. I want to use this to estimate the minimum airspeed required for normal flight 'without flaps'.

Improve this answer
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  • $\begingroup$ Yes these are usually available in $C_L$ - $C_D$ data. You would look those up for a particular wing cross section, just take an old NACA profile. By the way, it would have been better format had you posted the contents of this answer into your question, by editing it. $\endgroup$
    – Koyovis
    Commented Aug 13, 2017 at 4:24

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