shooting yourself down - more physics?

Smitty Two wrote:

1. I didn't stipulate a vacuum. My engine and wing don't work very well
without air. I said, to simplify calculations, ignore the effects of
friction on the projectile. We are flying above the earth.

You said discounting air friction. This is key to the problem. No air
friction would be the physical equivalent of being in a vacuum.

If there were no air friction, the projectile would continue ahead with
a forward speed of 1500 mph - its own 500 mph from its spent propellant
charge, and the 1000 mph imparted to it from the airframe.

Air friction, however, acts on the projectile from the moment it departs
the muzzle, and acts to slow the projectile in a continuous manner. The
aircraft continues to maintain its 1000 mph since it has a propulsive
device that is assumed to continue to operate. Air friction (along with
gravity) are the forces that conspire to ALLOW the aircraft to overtake
its projectile and contribute to shooting itself down.

So... are we or are we not including air friction? If we are, I am not
going to hazard a guess.. my math gland atrophied long ago after I
passed calculus. If we are not, then the problem is unsolvable in level
flight on earth.

Dave

In article t,
Dave S wrote:

Smitty Two wrote:

1. I didn't stipulate a vacuum. My engine and wing don't work very well
without air. I said, to simplify calculations, ignore the effects of
friction on the projectile. We are flying above the earth.

You said discounting air friction. This is key to the problem. No air
friction would be the physical equivalent of being in a vacuum.

If there were no air friction, the projectile would continue ahead with
a forward speed of 1500 mph - its own 500 mph from its spent propellant
charge, and the 1000 mph imparted to it from the airframe.

Air friction, however, acts on the projectile from the moment it departs
the muzzle, and acts to slow the projectile in a continuous manner. The
aircraft continues to maintain its 1000 mph since it has a propulsive
device that is assumed to continue to operate. Air friction (along with
gravity) are the forces that conspire to ALLOW the aircraft to overtake
its projectile and contribute to shooting itself down.

So... are we or are we not including air friction? If we are, I am not
going to hazard a guess.. my math gland atrophied long ago after I
passed calculus. If we are not, then the problem is unsolvable in level
flight on earth.

Dave

It's a hypothetical question, of course. I think I stated it fairly
clearly. Bill has already answered it correctly, with a second from
Alex. My calculus skills have also eroded over the years, which is one
reason I wanted to discount friction. But, I'd be curious to learn what
the real world answer would be, including friction, which of course is
dependent on a whole host of factors. (Of course, by the time the plane
caught up with the bullet in the real world, the friction would likely
have reduced its speed to something *relatively* harmless.)

Now, for some practical math, I hope one of these WW1 guys around here
can help me not shoot the prop off my RV when I put the .50 on the front.

Smitty Two wrote:
In article t,
Dave S wrote:

Smitty Two wrote:

1. I didn't stipulate a vacuum. My engine and wing don't work very well
without air. I said, to simplify calculations, ignore the effects of
friction on the projectile. We are flying above the earth.

You said discounting air friction. This is key to the problem. No air
friction would be the physical equivalent of being in a vacuum.

If there were no air friction, the projectile would continue ahead with
a forward speed of 1500 mph - its own 500 mph from its spent propellant
charge, and the 1000 mph imparted to it from the airframe.

...

So... are we or are we not including air friction? If we are, I am not
going to hazard a guess.. my math gland atrophied long ago after I
passed calculus. If we are not, then the problem is unsolvable in level
flight on earth.



Neglecting airfriction, the trajectory relative to the aircraft,
of the bullets fired from that aricraft will be the same
as the trajectory of bullets fired from a fixed position,
relative to that fixed position. As OP noted, the gunner hits
his own aircraft by firing staight up.

No Calculus required to reach that conclusion.


It's a hypothetical question, of course. I think I stated it fairly
clearly. Bill has already answered it correctly, with a second from
Alex. My calculus skills have also eroded over the years, which is one
reason I wanted to discount friction. But, I'd be curious to learn what
the real world answer would be, including friction, which of course is
dependent on a whole host of factors. (Of course, by the time the plane
caught up with the bullet in the real world, the friction would likely
have reduced its speed to something *relatively* harmless.)

That all depends on the relative velocity. If he fires upward and
forward and then does a low yo-yo to intercept I expect the bullets
could come down hard enough to hurt.


--

FF

(snip)
... my math gland atrophied long ago after I passed calculus.
(snip)

That calculus was *nasty* stuff ...
and matrix algebra was *worse*

I haven't recovered either, after 35+ years!

Peter

Peter Dohm wrote:
(snip)
... my math gland atrophied long ago after I passed calculus.
(snip)

That calculus was *nasty* stuff ...
and matrix algebra was *worse*

I haven't recovered either, after 35+ years!

Peter


Geeze, a buncha light weights. The calculus series and linear
algebra you guys took were rough? Differential equations? Hah! Take a
course in imaginary variables.

Dan, U.S. Air Force, retired