An Age Old Newton Ballistics Problem Solved

Yea he learned calculus at the age of 6. Just remember when it comes to dynamics in applied Newtonian Mechanics, nothing beats empirical data!
 
Americans should be ashamed that we are way down the list when compared to other countries in science education !! :mad: It's a great detriment to our countries future !
For the youngster -congratulations !! :)
For the rest of you - now you'll have the numbers but you'll still have to learn to shoot ! :rolleyes:
 
I'm wondering what age old problem that supposedly stumped Newton he solved.

Newton was very interested in the trajectory of objects as they traveled through a viscous medium, including air. But, I'm not sure he was puzzled by the math (that would be a laugh) or the combination of forces involved.

Based only on that article, it sounds like the lad figured out the ballistic coefficient and its application. We need more info on the problem and the solution.
 
I believe this is it, although my German was last exercised nearly 20 years ago.

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https://www.jugend-forscht.de/index.php/projectsearch/detail/6038.4568
 
Based only on that article, it sounds like the lad figured out the ballistic coefficient and its application. We need more info on the problem and the solution.
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No, it sounds like he found an exact solution.

Historically, once you threw drag into the mix you had to use various curve fitting algorithms. There was no "plug this number into this one little equation and get an answer". It was "plug this number into this *algorithm* and plug and chug and plug and chug and plug and chug...and get an approximate answer."

I seem to recall a Fourier series that did a similar stunt, but even that is an approximation.
 
Historically, once you threw drag into the mix you had to use various curve fitting algorithms. There was no "plug this number into this one little equation and get an answer". It was "plug this number into this *algorithm* and plug and chug and plug and chug and plug and chug...and get an approximate answer."
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My understanding too. Relative pressure varies, gravity varies accounting for those variations was always an issue. People who shoot things through the air long distances are going to be very interested in this.
 
I believe this is it
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MTT TL are you CERTAIN about this?

I ask because that's the same picture with the same equation my cable company showed me last time I questioned my bill.
 
Well, if we have gotten along without the formula for this long, I am not sure how much it is going to change our lives given that the really big long range guns have been replaced by missiles. Still, it is impressive, and not just one problem solved either.

I ask because that's the same picture with the same equation my cable company showed me last time I questioned my bill.
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Right, same equation. Ballistic trajectories and cable bill trajectories are very similar until apogee.
 
Sounds like long range shooters are going to have to pack more computers, calculators and slide rules to the range.

Problem is, by the time you get this all figured out, you're target is going to die of old age.
 
Here is the equation he solved:

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Finding the general solution to this differential equation will find the general solution for the path of a particle which has drag proportional to the square of the velocity (and opposite in direction).
Found Here

I guess what he did is find the general solution, rather than situationally specific solutions. (Most formulas of this type don't have general solutions or if they do we haven't found them.
 

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His work, while very commendable, will not be useful for general ballistics. He is working with particle dynamics. He does not account for bullet shape (drag coefficient), temperature, mass of the particle (the bullet), etc.
 
And it appears the fact that the actual shape of the drag curve as a function of velocity is a rather nasty non-linear expression around Mach 1 is not considered.

It rises approximately as v^2 below the speed of sound, flattens out near the speed of sound (about +/- 5-10% depending on shape), then starts decreasing above the speed of sound as the Mach angle reduces.

See Pejsa.

BC is NOT a constant, but varies with velocity and in a numerically non-continuous way.

An interesting solution to a very contrived theoretical problem.

Keep in mind Newton new nothing about changes in flow around the speed of sound.
 
Ah... instead of commending a youngster we hide our ignorance behind a wall of backhanded compliments.
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Who didn't commend the youngster and who gave him a backhanded compliment? You seem to be taking comments concerning the applicability of his accomplishment to the study of ballistics as negative comments. I don't believe they are meant that way in the least.

In fact, your comment is the only one approaching a negative comment in this thread.
 
Speaking as one who - once upon a time - used to do ballistics calculations for a living (Dept. of Defense).

His work, while very commendable, will not be useful for general ballistics. He is working with particle dynamics. He does not account for bullet shape (drag coefficient), temperature, mass of the particle (the bullet), etc.
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You say that as if any of the current methods DO account for all of the above. Or at least, as if they do it well. They don't.

They break it all down and treat all those entities as constants over brief periods of time..... Which you could also do for the kid's approach.

The difference is that to get reasonably accurate answers using the old approach, you have to use pretty small time steps.

If the kid's equation holds up to scrutiny, what you'd be able to do is combine his approach to the old school approach and use larger time steps to get more accurate results. That means reduced computational requirements.

That means more robust/cheaper electronics.

That means more accuate bombs (don't forget folks, that the bad guys use GPS jammers).

That means smaller/cheaper scopes that auto-correct the aim point.

It means all sorts of applications for the defense industry.
 
You say that as if any of the current methods DO account for all of the above. Or at least, as if they do it well. They don't.
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That is not at all what I said or implied. I give up.
 
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