Physics question

There is a (magic) B-17 flying along at 560 mph. The tail gunner is out of
..50 caliber ammo. He sees a Messerschmitt ME-109 crossing behind the B-17,
50 yards away.

He pulls out his trusty .45 Colt auto (muzzle velocity 820 fps) and fires at
the Hun when the ME-109 is directly behind the B-17. He leads the
Messerschmitt by exactly enough to hit the pilot (if he were firing from a
fixed position).

Does the bullet exit the muzzle and fall directly to earth?

Rich "Scratching my head" S.

No, the ME-109 has zero relative velocity in the B-17s flight path...he said
CROSSING 50 yards behind the aircraft.

Jim



"T o d d P a t t i s t" wrote in message
...
"Rich S." wrote:

Does the bullet exit the muzzle and fall directly to earth?

Yes, aside from the tiny diff between 560 mph and 820 fps,
assuming he pointed directly backwards and that there was no
wind. The ME-109 flies into the falling bullets.

In article ,
"Rich S." wrote:

There is a (magic) B-17 flying along at 560 mph. The tail gunner is out of
.50 caliber ammo. He sees a Messerschmitt ME-109 crossing behind the B-17,
50 yards away.

He pulls out his trusty .45 Colt auto (muzzle velocity 820 fps) and fires at
the Hun when the ME-109 is directly behind the B-17. He leads the
Messerschmitt by exactly enough to hit the pilot (if he were firing from a
fixed position).

Does the bullet exit the muzzle and fall directly to earth?

Rich "Scratching my head" S.


Yes, but the bullet is traveling at 820 ft/s relative to the B-17. The
bullet will drop straight down, but can still hit the ME, which runs int
the bullet.

"T o d d P a t t i s t" wrote in message
...
"RST Engineering" wrote:

No, the ME-109 has zero relative velocity in the B-17s flight path...he
said
CROSSING 50 yards behind the aircraft.

True, he said "crossing," but he also said he's leading the
ME-109, and I specified that he fires straight back, i.e.,
he leads the ME-109 so that he's aiming at the point where
the ME-109 crosses the B-17s flight path.

The bullet drops straight down (relative to the ground).
The ME-109 flies into it before it drops significantly.

Perhaps I wasn't clear. Maybe I can diagram it.

Aiming
point
. ----- ME-109

B-17
|
V

This means that the turret gunner would have a problem in judging trajectory
to a target which passes by either front-to-rear or vice versa. Perhaps the
slower velocity of the bomber (in real life) and the higher velocity of a
..30 cal or .50 cal bullet would minimize the correction necessary. Then too,
that's why they make tracers!

Rich "I think I see" S.

T o d d P a t t i s t wrote:
"RST Engineering" wrote:

No, the ME-109 has zero relative velocity in the B-17s flight path...he said
CROSSING 50 yards behind the aircraft.

True, he said "crossing," but he also said he's leading the
ME-109, and I specified that he fires straight back, i.e.,
he leads the ME-109 so that he's aiming at the point where
the ME-109 crosses the B-17s flight path.

There is "leading" and there is "leading correctly". It makes
no sense to state the former without implying the latter so
the question reduces to whether or not it is *possible*
to hit, since if the gunner leads *correctly* he will
hit by the definition of *leading*.


The bullet drops straight down (relative to the ground).
The ME-109 flies into it before it drops significantly.

If by crossing we mean the ground tracks are orthogonal and
if it was already behind the B17 when the shot was fired
then without a velocity component parallel to the
flight path of the B17 the Me-109 will always cross the
flight path of the B17 *behind* the point where the shot
was fired. The gunner cannot hit the ME 109 in those
circumstances.

The gunner has to fire (and I got this wrong a minute ago)
at the moment the flight path of the B17 (actually at the
moment the muzzle of his gun) crosses the flight
path of the ME 109 ahead of the Me 109, and at the correct
elevation angle to compensate for differences in altitude,
and rate of climb of the Me-109 relative to the B17, keeping
in mind that the changes in elevation angle will also affect
the horizontal compenants of the bullet's velocity.

--

FF

Rich S. wrote:
"T o d d P a t t i s t" wrote in message
...
"RST Engineering" wrote:

No, the ME-109 has zero relative velocity in the B-17s flight path...he
said
CROSSING 50 yards behind the aircraft.

True, he said "crossing," but he also said he's leading the
ME-109, and I specified that he fires straight back, i.e.,
he leads the ME-109 so that he's aiming at the point where
the ME-109 crosses the B-17s flight path.

The bullet drops straight down (relative to the ground).
The ME-109 flies into it before it drops significantly.

Perhaps I wasn't clear. Maybe I can diagram it.

Aiming
point
. ----- ME-109

B-17
|
V


In your text you said the gunner fies when the ME 109
is directly behind the B17. For orthogonal ground
tracks, he cannot hit the ME 109 if it is *anywhere* behind
the B17 no matter where he aims because the flight
paths of the ME 109 cannot intersect the path
the bullet takes to the ground.


In your illustration, the gunner fires straight back
before the Me-109 is directly behind the B17. He can hit
if he fires at precisely the moment his gun crosses the
flight path of the Me-109.

--

FF

wrote in message
oups.com...

In your text you said the gunner fies when the ME 109
is directly behind the B17. For orthogonal ground
tracks, he cannot hit the ME 109 if it is *anywhere* behind
the B17 no matter where he aims because the flight
paths of the ME 109 cannot intersect the path
the bullet takes to the ground.

That's why, in the text, I also added that he "led" the ME-109 exactly
enough. Did you read the entire sentence? As I said, perhaps I wasn't clear.
He fires directly behind the B-17. The ME-109 is on its way to cross the
flightpath of the B-17.

In your illustration, the gunner fires straight back
before the Me-109 is directly behind the B17. He can hit
if he fires at precisely the moment his gun crosses the
flight path of the Me-109.

Not so. The bullet simply falls to Earth and the ME-109 passes safely 50
yards (or so) behind the B-17.

Rich "Don't use them 3-silable words like 'orthogonal'" S.

He misses the ME-109 because the recoil of firing the bullet
accelerates the B-17 just a bit, so that the bullet, travelling at a
little less than the bomber's speed actually briefly follows the bomber
as it falls.

A related question: Haven't there been cases of supersonic
fighters shooting themselves down when they caught up to the shells
they'd fired forward?

Dan

With bullet/plane(s) relative horizontal speed of 820ft/s, the other
plane reaches the bullet position in (50x3)/820 = 0.183 sec (pretty
slow bullet). In that time the bullet falls a vertical distance of 0.5
x 32 x 0.183 x 0.183 ft = 0.536 ft. If the messer plane bottom was at
least 0.537 ft (about 7 inches) below bullet firing vertical position
its gona hit the other plane.

Ignoring air friction, whether the planes are moving or parked on the
ground with same separation it does not matter. It is only the relative
velocity of the bullet to the planes that counts. But with backward
airstream and downward friction the bullet will fall slower down than
in vacuum - so better chance of hitting the plane behind.

Is this your night school physics home assignment and you are cheating
here?

Rich S. wrote:
wrote in message
oups.com...

In your text you said the gunner fies when the ME 109
is directly behind the B17. For orthogonal ground
tracks, he cannot hit the ME 109 if it is *anywhere* behind
the B17 no matter where he aims because the flight
paths of the ME 109 cannot intersect the path
the bullet takes to the ground.

That's why, in the text, I also added that he "led" the ME-109 exactly
enough. Did you read the entire sentence?

Yes, you added the condition that he leads by exactly the same
amount he would from a fixed condition to the statement that
he fires when the ME-109 is directly behind the B17.
If he waits to fire until after the B17 has crossed the
flight path of the ME 109 he cannot hit no matter how
he aims. It matters not how he leads.


As I said, perhaps I wasn't clear.
He fires directly behind the B-17. The ME-109 is on its way to cross the
flightpath of the B-17.

This you added in a later post. If, while firing straight back
he still leads as if he were firing from a fixed position he
will miss again because the B17 has already crossed the flight
path of the ME-109 by the time he fires.

No matter the direction, if he fires after the B17 has
crossed the flightt path of the ME-109 he misses.



In your illustration, the gunner fires straight back
before the Me-109 is directly behind the B17. He can hit
if he fires at precisely the moment his gun crosses the
flight path of the Me-109.

Not so. The bullet simply falls to Earth and the ME-109 passes safely 50
yards (or so) behind the B-17.

That is true if he leads the ME109 as he would from a fixed
position, or any way other than the *right* way. But there
is a right way. I *changed* the scenario when I said he
fires at precisely the moment his gun crosses the flight
path of the ME-109.

If he fires stright back at that moment,
and the ME 109 is flying at the same airspeed as
the B-17 then the bullet is *also* 50 yards behind the
B17, when the ME-109 crosses. It will be a half inch or
so lower than the altitude at which it exited the muzzle
if it was fired exactly level.

Firing straight back at the moment the B17 crosses the
flight path of the ME-109 essentially drops the bullet
through the flight path of the ME-109. IF the bullet is
still there when the ME-109 arrives, which it will be
for a range of speeds close the speed of the B17,
the gunner hits.

An the gunner can compensate for the ME-109 flying
at a different speed and altitude by firing up or
down a little, again for some range of speeds and
altitudes.

--

FF