shooting yourself down - more physics?

[Smitty Two]

If you guys aren't tired of arithmetic, I'm wondering if any fighter
pilots have shot themselves down. Probably not, but imagine you're
flying straight and level at 1000 mph and fire a 500 mph projectile at
an enemy that's directly ahead but at a higher altitude. You miss him;
the bullet follows a parabolic path, returning to your altitude just as
you overtake it. Discounting air friction, at what angle was the bullet
fired?

(extra credit question -- how many rivets could you have installed in
the time you wasted thinking about this question?)

[Flyingmonk]

>what angle was the bullet fired?

I'd suspect that the caliber - the loading of the bulltets (propellent
and bullet weight and shape) would have influence onn the outcome as
well ~> to answer your question.

>extra credit question --

Five carefully measured and placed, 50 if placed haphazardly. This
also depends on the dificulty of the location of rivets to be
installed.

Bryan "The Monk" Chaisone

[Bill Chernoff]

Discounting air friction, at what angle was the bullet
> fired?
>

Discounting air friction the angle would be 90 degrees, straight up.

[Rich S.]

Smitty Two asked:

> If you guys aren't tired of arithmetic, I'm wondering if any fighter
> pilots have shot themselves down. Probably not, but imagine you're
> flying straight and level at 1000 mph and fire a 500 mph projectile at
> an enemy that's directly ahead but at a higher altitude. You miss him;
> the bullet follows a parabolic path, returning to your altitude just as
> you overtake it. Discounting air friction, at what angle was the bullet
> fired?

Before you find yourself in the same trap as me, let me ask for some
clarification:

1. Since you stipulate a vacuum, are we flying above the Earth?
2. How high?
3. Are we flying at an absolute altitude, e.g. following an orbital path?
4. Is the plane flying level at the moment of firing with only the gun
pointed up at the target airplane?

Rich "Without a clue" S.

[Smitty Two]

In article >,
"Rich S." > wrote:

> Smitty Two asked:
>
> > If you guys aren't tired of arithmetic, I'm wondering if any fighter
> > pilots have shot themselves down. Probably not, but imagine you're
> > flying straight and level at 1000 mph and fire a 500 mph projectile at
> > an enemy that's directly ahead but at a higher altitude. You miss him;
> > the bullet follows a parabolic path, returning to your altitude just as
> > you overtake it. Discounting air friction, at what angle was the bullet
> > fired?
>
> Before you find yourself in the same trap as me, let me ask for some
> clarification:
>
> 1. Since you stipulate a vacuum, are we flying above the Earth?
> 2. How high?
> 3. Are we flying at an absolute altitude, e.g. following an orbital path?
> 4. Is the plane flying level at the moment of firing with only the gun
> pointed up at the target airplane?
>
> Rich "Without a clue" S.

I think I'm already in that trap, but it wasn't my intention (or yours,
I know) for this to be a trick question based on ambiguity in the
phrasing.

But, sure, I'll address your concerns.

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.

2. At an altitude at which acceleration due to gravity is 32 feet per
second per second. Assume this remains constant throughout.

3. With the exception of the airplanes and the guns, this is a
pre-Columbian question. The earth is flat. Or, if you prefer, we're
flying tangentially to its curved surface.

4. The plane is flying level, as I believe I stated.

[Rich S.]

"Smitty Two" > wrote in message
...

> I think I'm already in that trap, but it wasn't my intention (or yours,
> I know) for this to be a trick question based on ambiguity in the
> phrasing.
>
> But, sure, I'll address your concerns.
>
> 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.
>
> 2. At an altitude at which acceleration due to gravity is 32 feet per
> second per second. Assume this remains constant throughout.
>
> 3. With the exception of the airplanes and the guns, this is a
> pre-Columbian question. The earth is flat. Or, if you prefer, we're
> flying tangentially to its curved surface.
>
> 4. The plane is flying level, as I believe I stated.

Kewl! That makes it easy!

I don't know.

Rich S.

[Matt Whiting]

Bill Chernoff wrote:
> Discounting air friction, at what angle was the bullet
>
>>fired?
>>
>
>
> Discounting air friction the angle would be 90 degrees, straight up.

But that would neglect the coriolis force... :-)

Matt

[Rick Marvin]

I remember reading of a F-104 Starfighter pilot who shoot himself down.
He tested his guns, then accelerated, nose down and ran into his own
shells.

On Sat, 10 Sep 2005 12:21:29 -0400, Smitty Two >
wrote:

> If you guys aren't tired of arithmetic, I'm wondering if any fighter
> pilots have shot themselves down. Probably not, but imagine you're
> flying straight and level at 1000 mph and fire a 500 mph projectile at
> an enemy that's directly ahead but at a higher altitude. You miss him;
> the bullet follows a parabolic path, returning to your altitude just as
> you overtake it. Discounting air friction, at what angle was the bullet
> fired?
>
> (extra credit question -- how many rivets could you have installed in
> the time you wasted thinking about this question?)

--
Using Opera's revolutionary e-mail client: http://www.opera.com/mail/

[alexy]

"Bill Chernoff" > wrote:

> Discounting air friction, at what angle was the bullet
>> fired?
>>
>
>Discounting air friction the angle would be 90 degrees, straight up.

Yep. I was going to say "impossible" since he was firing at a plane
ahead of him, and I incorrectly translated that to a barrel angle with
some forward component. But you are right, the 90-degree angle may
well have been the firing solution for the target ahead of him, given
differences in the plane's velocities. Glad I read your correct answer
before giving my answer of "impossible"!
--
Alex -- Replace "nospam" with "mail" to reply by email. Checked infrequently.

[Capt. Geoffry Thorpe]

"Smitty Two" > wrote in message
...
> If you guys aren't tired of arithmetic, I'm wondering if any fighter
> pilots have shot themselves down. Probably not, but imagine you're

I know a guy who got shot down by his own waist gunner in a B-24, does that
count?

(The gun mount broke and the gunner didn't let go of the trigger as he (and
the gun) fell backwards...)

--
Geoff
the sea hawk at wow way d0t com
remove spaces and make the obvious substitutions to reply by mail
Spell checking is left as an excercise for the reader.

[Dave S]

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

[Smitty Two]

In article >,
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.

[Jeff]

Has nothing to do with physics, but it is possible for a helicopter to shoot
himself down in several different ways. Fire a pair of 2.75" rockets at the
same time with proximity fuses while doing running fire and it could get
ugly.

Running fire while shooting the gun (or rockets) at close ranges could
easily produce ricochets that could hit the helicopter. I have seen the 50
caliber machine gun on an OH-58D blow out the copilot chin bubble before.

Another good way to shoot yourself down is for one helicopter to remote
LASER designate for another helicopter firing a Hellfire missile while you
are inside a certain fan in front of the firing helicopter. The Hellfire
can lock on to the laser designating source rather than the target.

Jeff
recently retired Army CW4 Master Army Aviator

"Smitty Two" > wrote in message
...
> If you guys aren't tired of arithmetic, I'm wondering if any fighter
> pilots have shot themselves down. Probably not, but imagine you're
> flying straight and level at 1000 mph and fire a 500 mph projectile at
> an enemy that's directly ahead but at a higher altitude. You miss him;
> the bullet follows a parabolic path, returning to your altitude just as
> you overtake it. Discounting air friction, at what angle was the bullet
> fired?
>
> (extra credit question -- how many rivets could you have installed in
> the time you wasted thinking about this question?)

[Dan, U.S. Air Force, retired]

Jeff wrote:
> Has nothing to do with physics, but it is possible for a helicopter to shoot
> himself down in several different ways. Fire a pair of 2.75" rockets at the
> same time with proximity fuses while doing running fire and it could get
> ugly.
>
> Running fire while shooting the gun (or rockets) at close ranges could
> easily produce ricochets that could hit the helicopter. I have seen the 50
> caliber machine gun on an OH-58D blow out the copilot chin bubble before.
>
> Another good way to shoot yourself down is for one helicopter to remote
> LASER designate for another helicopter firing a Hellfire missile while you
> are inside a certain fan in front of the firing helicopter. The Hellfire
> can lock on to the laser designating source rather than the target.
>
> Jeff
> recently retired Army CW4 Master Army Aviator
>
During WW2 P-51s shot them selvesdown when making low level passes
and debris got scooped into the oil cooler.

Dan, U.S. Air Force, retired

[Peter Dohm]

(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

[Ken Chaddock]

Smitty Two wrote:

> If you guys aren't tired of arithmetic, I'm wondering if any fighter
> pilots have shot themselves down. Probably not, but imagine you're
> flying straight and level at 1000 mph and fire a 500 mph projectile at
> an enemy that's directly ahead but at a higher altitude. You miss him;
> the bullet follows a parabolic path, returning to your altitude just as
> you overtake it. Discounting air friction, at what angle was the bullet
> fired?
>
> (extra credit question -- how many rivets could you have installed in
> the time you wasted thinking about this question?)

What kind of gun do *you* have with a muzzle velocity of only 733 fps ?

....Ken

[Dave S]

Jeff wrote:

The Hellfire
> can lock on to the laser designating source rather than the target.
>
This is what the post-accident investigators refer to as "a very bad
thing" (TM).

Dave

[Flyingmonk]

..22 shooting CB caps.

[Dan, U.S. Air Force, retired]

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

[Dan, U.S. Air Force, retired]

Ken Chaddock wrote:

> Smitty Two wrote:
>
>> If you guys aren't tired of arithmetic, I'm wondering if any fighter
>> pilots have shot themselves down. Probably not, but imagine you're
>> flying straight and level at 1000 mph and fire a 500 mph projectile at
>> an enemy that's directly ahead but at a higher altitude. You miss him;
>> the bullet follows a parabolic path, returning to your altitude just
>> as you overtake it. Discounting air friction, at what angle was the
>> bullet fired?
>>
>> (extra credit question -- how many rivets could you have installed in
>> the time you wasted thinking about this question?)
>
>
> What kind of gun do *you* have with a muzzle velocity of only 733 fps ?
>
> ...Ken

A light 45, old 38 S&W, 38 rimfire, 45-70....

Dan, U.S. Air Force, retired

[Dan, U.S. Air Force, retired]

Flyingmonk wrote:

> .22 shooting CB caps.
>
.22 short gallery. I may have the last box of that stuff in the world.

Dan, U.S. Air Force, retired

[[email protected]]

Dan, U.S. Air Force, retired wrote:
> Ken Chaddock wrote:
>
> >..
> >
> > What kind of gun do *you* have with a muzzle velocity of only 733 fps ?
> >
> > ...Ken
>
> A light 45, old 38 S&W, 38 rimfire, 45-70....
>

Back when my eyesight was better I could look over the left
shoulder of a right-handed shooter so that his body blocked
most of the muzzle flash and see the bullets traveling
downrange thanks to the foreshortening effect. This was
with Auto Ordinance's version of the 1911-A at a well-lit
indoor range.

Haven't tried that lately.

--

FF

[[email protected]]

Smitty Two wrote:
> In article >,
> 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