# The effect of gravity on a speeding bullet

Discussion in 'Physics & Math' started by Magical Realist, Jan 31, 2017.

1. ### exchemistValued Senior Member

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I think the point is that in the OP scenario we are not in deep space but simply high above the Earth. If that is the case, then a bullet will be subject to the Earth's gravity and will accelerate, as Origin says.

Of course if we were in deep space, remote from any gravitational effects, then what you say would be true.

3. ### Michael 345Looking for Bali in NovValued Senior Member

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So I am not loosing my mind

Thanks

Fall to Earth accelerating might have helped

So no hallucination about a train either right?

5. ### exchemistValued Senior Member

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There were no trains in the OP.

7. ### Michael 345Looking for Bali in NovValued Senior Member

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True

But there was in a post a little later

Is there a rule only to send post which only relates to the original post?

8. ### river

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Earlier you mean .

# the post .

9. ### Michael 345Looking for Bali in NovValued Senior Member

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Original post above

Post number 14 above

Unless my mathmatics has failed me 14 comes after 1

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No

11. ### sculptorValued Senior Member

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entertaining back of the envelope morning calc..

300 win mag, 3200 fps muzzle velocity = about 2181 mph just a tad shy of the speed of the sr71 blackbird about 2200 mph.
That is one damned fast train...........a true "bullet train"?
so add the 2181 mph to 2181 mph gives us a bullet speed of 4362 mph, about 6M
WOW
Would that create enough friction to burn up the bullet?
(space shuttle reentry was just a tad under 25M)

...............
OK I'm gonna make some more coffee anyone want some?

12. ### Michael 345Looking for Bali in NovValued Senior Member

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White no sugar thanks

Can I peek at the envelope?

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idiom

14. ### RajeshTrivediValued Senior Member

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after the second post by origin, the thread is almost free for all. So many irrelevant posts.

The question involving drag force on bullet is very complex, and has no straightforward answer. The OP adds to complexity wherein the simple answer as given by origin may not, repeat may not, hold.

When I saw the terminal velocity term, it reminded me of Millikan Oil Drop experiment, but the case here is very different and involves many factors.

1. The aircraft altitude, say 40000 ft, around 12000 meters.
2. The speed of the aircraft, say around 200 meters per seconds.
3. The air density at that altitude and variation in air density as the altitude falls.
4. The speed of bullet, supersonic, say around 700 meters seconds.
5. The direction of shot : Downwards in aircraft frame.
6. The bullet drop speed at which the gravitational acceleration and drag deceleration would become equal. This depends on the bullet mass and design.

So in this case the bullet will acquire the terminal speed in downwards direction (as per 6) iff the horizontal component of its speed which was 200 meter per second at start would become zero due to air drag in horizontal direction. The question is will the horizontal component become zero from 200 meter per seconds before it completes the vertical distance of 12000 meters and hits the ground?

So the answer is since the air drag deceleration is higher as compared to gravitational acceleration at those speeds, the bullet will surely slow down, but it may not achieve the terminal constant speed before hitting the ground.

15. ### originIn a democracy you deserve the leaders you elect.Valued Senior Member

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The OPs question is simple and straight forward as is the answer.
See, simple and straight forward. [shrug]

16. ### RajeshTrivediValued Senior Member

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If it is so simple, as you are claiming, then take the mass of bullet as 4 grams, altitude as 40000 ft, pressure change from 100% at earth surface to 25% at 40000 ft, bullet velocity at 700 meter per seconds, aircraft velocity at 200 m/sec. Now please caluclate the altitide where it will attain the terminal speed. Can you?

17. ### originIn a democracy you deserve the leaders you elect.Valued Senior Member

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I can do that calculation but I certainly am not going to take the time and effort to do it (as I pointed out it involves a nonlinear differntial equation).

But the point remains that the OPs question was straight forward and the answer is straight forward and not complicated.

I assume this is where we are supposed to get into some annoying argument about some obtuse point about this or that, but I really do not feel like it.

Last edited: Feb 6, 2017
paddoboy, sweetpea and exchemist like this.
18. ### KittamaruNever cruel nor cowardly...Staff Member

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Before demanding Origin start utilizing his time performing lengthy (and in all honesty, utterly needless in the context of this thread) equations...

Why are you asking him to do this? Are you disputing the validity of his claim?

19. ### OphioliteValued Senior Member

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No, but for the bulk of this thread you had lost your reading comprehension. Don't misinterpret exchemist's efforts to restore calm to the situation as unwavering support for your position. You are in danger of becoming seriously obtuse.

20. ### RajeshTrivediValued Senior Member

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Pl refer to my post #51. He made a claim that it is simple and terminal velocity will be achieved, that response is at the best cursory, he must show how it is simple and how it will achieve terminal speed. So simple. Isn't it?

And BTW what makes you think that in science section such calculations will be "utterly needless" ? You, being a staff member, are giving an impression that this forum is for casual chit chat only (even the sceince section).

And yes for your information, the problem is not so simple, its a complex physics problem involving fluid mechanics, gravity, design and mass of bullet, pressure and temperature variation, supersonic speeds.

21. ### RajeshTrivediValued Senior Member

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No you cannot, its not even available in literature analytically. It is very complex. There is no harm in discussing something in depth, your answer was indicative.

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No harm indeed if the questioner required it, and it was given without any notable agenda.

23. ### originIn a democracy you deserve the leaders you elect.Valued Senior Member

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Of course it is available. Here is an analysis that I quickly found.
You will notice that the analysis assumed a linear differential equation instead of a nonlinear one. This is an acceptable method to determine terminal velocity for a relatively slow moving object.
In your example the speed of the plane/bullet in the direction parallel to the ground can be ignored. The bullet is initially at supersonic speed so the actual analysis must include the nonlinear aspect of friction. This is also available in literature. It is not easy due to the nonlinear aspect of the friction but there are many numerical methods to closely approximate the solution.
If you are interested you can google "(non)linear equations and terminal velocity".
If you are really, really interested get a text book from the library on Differential Equations or a text book on Aeronautical Engineering and you could probably find a example similar to yours explained.
Have fun.