# Supersonic drag force

#### mccaly

Hey,

I am trying to calculate the drag force on netting at supersonic speeds. currently I have been using the equation:

F = 1/2 (ρ V² Cd A)

I am having trouble applying it to netting due to the drag coefficiant, since i cannot find one for netting. Also all the examples I have seen for this equation have been for subsonic velocities, can I still apply to supersonic?

The force will only be applied to a short period of time i.e 25ms due to it coming from an explosion.

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#### russ_watters

Mentor
No, the drag force is completely different at supersonic speed. The primary component is the "wave drag", which is the compression due to the creation of the shock waves.

Drag coefficient isn't easy to find methematically. It is typically found experimentally except in the case of sophisticated computer modeling.

#### mccaly

I thought that may be the case with the coefficiant.

I will have a look and see what I can find on 'wave drag'

thanks.

#### jaap de vries

Yes the oblique shock in the case of a slender (sharp) body creates pressure drag sometimes called wave drag. The drag of a slender body at subsonic speeds is mostly friction drag.

Be aware do that at supersonic speeds, the drag coefficient is still calculated by normalizing the drag with respect to the dynamic pressure (0.5 * rho * V^2)

So using your equation should work if the drag coefficient is calculated for supersonic speeds.

#### mccaly

Yes the oblique shock in the case of a slender (sharp) body creates pressure drag sometimes called wave drag. The drag of a slender body at subsonic speeds is mostly friction drag.

Be aware do that at supersonic speeds, the drag coefficient is still calculated by normalizing the drag with respect to the dynamic pressure (0.5 * rho * V^2)

So using your equation should work if the drag coefficient is calculated for supersonic speeds.

I dont have the equipment to find the coefficiant experimentaly. Could you expand on how I would calculate it, sorry if I am being slow.

#### h2oski1326

I think you should provide more detail on the project/problem you are describing.

An explosion, 25ms? Is this object accelerating to Supersonic speeds or being dropped suddenly into a supersonic flow? What range of Mach numbers are you talking about? What is the size of the net material relative to the spacing between each section?

Traditional gas dynamics analysis assumes some things like steady flow with a non-accelerating frame of reference. This may make it very difficult to analyze your problem analytically. It sounds like making those assumptions in your situation may not be acceptable and thus any work you do to find a Cd analytically may not be valid.

#### mccaly

it would be dropped into a supersonic flow in the mach 1.5-2.5 region. the material itself would have a 50% open to 50% material spacing.

the explosion itself, for an example could have a positive phase duration of 25 ms.

#### h2oski1326

There are a few problems I see if trying to approach this problem with a simple 'back of the envelope' type analysis.

1) It sounds like your netting would create a pretty broad surface for the flow to impact. So you are likely to get the formation of normal shocks, curved normal shocks, and some oblique shocks and likely some interaction of shock waves.

The increase in pressure across a normal shock is much higher than that of an oblique shock and increases as the Mach number becomes more supersonic. This could change your results drastically depending on the situation.

2) As stated previously, traditional gas dynamics relations across shocks assume steady flow of a non-accelerating reference frame; I am not sure if either apply here.

If you wanted a rough, high-end estimate you could assume a simple normal shock has formed off the bow of each section of net, the flow is 1D, steady, and the net is not accelerating. Then by using the information you know about the incoming flow you could find the pressure increase across the shock using some http://en.wikipedia.org/wiki/Normal_shock_tables" [Broken]. Finding a drag coefficient is then a matter of performing a force balance on your net to find the force due to pressure drag your net feels. Writing this force in a dimensional form using the equation you provided above may give you an idea what range you may be in.

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#### jaap de vries

What you could do is calculate the pressure rise after a normal shock
Equations for which are rather lengthy but are typically a function of gamma and M.

Blunt body aerodynamics is not a trivial problem. in the 50's and 60's millions of dollars on research were spend to solve this to no avail. However, in 1966 Moretti and Abbet were the first to solve it using CFD. Now, using FLUENT or similar this problem should not be hard to solve since viscosity can be neglected and the Euler equation can be utilized.

ref: J.D. Anderson, "Computational Fluid Dynamics" 1995.

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