Force that a car-mounted flag would produce

[kspabo]

Let's say I have a 15-lb flag that is mounted to a car on a welded bracket. I want to know the general force the flag will exert on the bracket (neglecting flex in the flag, assuming uniform weight throughout) in the scenario of let's say braking at max speed (as this is the most simple situation to calculate this). You're going 75 MPH, slam on the brakes and stop within 3 seconds.

I tried doing some really simple hand calcs myself (f=ma=m*dv/dt) but I realize this is the incorrect method (as my numbers were unrealistic)

To give you a better idea of why, I'm trying to design a flag mount for a car that pivots and has a lock pin the keeps it in position. I'm looking to see the chance of failure in this pin.

 

[mfb]

F=ma is fine for braking. Use SI units if you want neat unit conversions.

Torque will probably be more important than the force.

A 15 pound flag? What is the expected drag of this massive flag?

 

[anorlunda]

The flag will be flapping wildly. The shock wave of each flap will be transferred to the bracket. I don't know how to calculate the max instantaneous force.

See this earlier thread

https://www.physicsforums.com/threads/tatterproof-flag-design-needed.686921/#post-4354976

Edit: the bracket might not be the biggest problem. Tattering will destroy the flag in a short time.

 

[Mech_Engineer]

The worst-case force on the bracket will be induced by drag on the flag, not the stopping force during deceleration. I recommend estimating the drag of the flag and pole and then design your bracket with a strong safety factor from there.

 

[CWatters]

This page looks useful..

https://www.lmnoeng.com/Force/DragForce.php

..but you would have to review the paper on which its based. For example I don't know if it gives you an average drag force or a peak drag force due to the fluttering of the flag.

 

[anorlunda]

Your problem is analogous to sizing a flagpole based on flag size and wind speed.

You didn't say how high your flagpole is that is key because you create a twisting force on the bracket with a long lever arm.. I'm guessing a 6x10 flag weighs about 15 pounds. It would have been better for you to give the flag size.

Here is a table of flagpole wind speed ratings that may be helpful. https://www.eaglemountainflag.com/content/flagpolewind

The shortest one in the table for a 6x10 flag is a 7 inch diameter0 pole with 0.156" walls. In other words huge. But that's for 40 feet pole rated for 120 mph and bedded in the ground with cement.

How to scale that down to a 6 foot pole rated 75 mph welded to the car? Multiply by $(6/40)*(75/120)^2=0.06$? I'm not sure.

Maybe you could search for banner bracket ratings. The kinds of brackets used to attach banners to utility poles.

For a completely different approach that suggests much thinner flag poles, consider this crazy. The forces he's holding look pretty modest.