[imatfaal]

Projectiles go furthest in the horizontal plane for a given muzzle velocity when fired at 45degrees to the horizontal (although I think this angle ignores air resistance)  - but the muzzle velocity itself is independent of the angle of inclination.

[RE.Craig]

Projectiles go furthest in the horizontal plane for a given muzzle velocity when fired at 45degrees to the horizontal (although I think this angle ignores air resistance)  - but the muzzle velocity itself is independent of the angle of inclination.

Surely a projectile fired in the horizontal would hit the earth sooner since it,s trajectory means that it begins to fall the moment it leaves the barrel?

[RE.Craig]

As I thought 90 degrees hits the ground before the  45 degree vector and 45 degrees has the absolute range of any cannon fired projectile .[/i]http://www.physicsclassroom.com/mmedia/vectors/mr.cfm

[CliffordK]

Projectiles go furthest in the horizontal plane for a given muzzle velocity when fired at 45degrees to the horizontal (although I think this angle ignores air resistance)  - but the muzzle velocity itself is independent of the angle of inclination.

Reread imatfaal's post.
He is in fact suggesting to get horizontal distance, one must fire gun at an angle.

However, in the case of the HARP gun, the goal is to reach > 100 miles in altitude.  In this case, a nearly vertical launch is preferable to minimize the time and air to pass through to reach "space".  However, it should be noted that while the projectile may reach 100 miles altitude, it is not traveling in a trajectory, or at a velocity that would allow to it remain in orbit.

Keep in mind that downward acceleration at about 9.8 m/s² is related directly to time, so the more time from launch, the greater the loss of vertical velocity.  And, of course, firing it at an angle, the vertical component of the velocity vector begins lower.  And, the more time at lower altitudes, the greater the wind resistance further decreasing velocity.

Thus, for maximum vertical altitude, one benefits from a vertical launch (assuming one is not using wings to create lift).

[Bored chemist]

As far as I am aware a gun can achieve it's greatest velocity when fired at an angle of  45°. If this is the case what speed and distance would the projectile [that reached an altitude of 112 miles fired at near 90°] have attained had it been fired at 45°?

As far as I remember a gun will have it's greatest range , for a given muzzle velocity, when it's at 45 degrees (assuming a few things, notably a flat earth).
If I wanted the greatest muzzle velocity, I would point it down. gravity might not help much, but it would help.

In the real world, the usual model* for range doesn't work terribly well. The biggest problem is that it ignores air resistance.
If you are trying to ram air out of the way at hypersonic speeds, air resistance is hugely important.
45 degrees is no longer the "right " answer and a calculation of the range isn't going to be very good.
As an indication, the (lower bound to the) velocity I calculated for the HARP projectile was 1700 m/s. The real speed was about twice that.
* Like this
http://en.wikipedia.org/wiki/Trajectory#Uniform_gravity.2C_no_drag_or_wind

[CliffordK]

One would note that mortars are frequently fired at high angles.

This probably gives 3 things.

• Going over obsticles
• Gaining Distance
• Adjusting range using a fixed propellant load

[RE.Craig]

As far as I am aware a gun can achieve it's greatest velocity when fired at an angle of  45°. If this is the case what speed and distance would the projectile [that reached an altitude of 112 miles fired at near 90°] have attained had it been fired at 45°?

As far as I remember a gun will have it's greatest range , for a given muzzle velocity, when it's at 45 degrees (assuming a few things, notably a flat earth).
If I wanted the greatest muzzle velocity, I would point it down. gravity might not help much, but it would help.

In the real world, the usual model* for range doesn't work terribly well. The biggest problem is that it ignores air resistance.
If you are trying to ram air out of the way at hypersonic speeds, air resistance is hugely important.
45 degrees is no longer the "right " answer and a calculation of the range isn't going to be very good.
As an indication, the (lower bound to the) velocity I calculated for the HARP projectile was 1700 m/s. The real speed was about twice that.
* Like this
http://en.wikipedia.org/wiki/Trajectory#Uniform_gravity.2C_no_drag_or_wind

You say [if I read you right] that in the real world firing the projectile at 45 degrees s no longer the "right" answer! At what angle in your world would you fire the gun for maximum range?

[Bored chemist]

How long is a piece of string?
If the velocity is over about 11 km/s the question is meaningless: you never see the projectile again.
Are you shooting with, or against the rotation of the earth (or at an angle to it?)
It really isn't a trivial question with a "best" answer.
http://en.wikipedia.org/wiki/External_ballistics

[imatfaal]

Whilst I agree with the piece of string answer - too wide a question to admit to an answer - you could look at an example from history.  During the great war the germans bombarded Paris with a huge siege gun from around 120 Km away.  The angle of inclination of the Paris Gun was 55 degrees; but whether this was optimal, an engineering/technological requirement, or just the angle calculated to drop shells on Paris is not something I can tell you

http://en.wikipedia.org/wiki/Paris_Gun

[RE.Craig]

I would imagine they fired the gun at 55* to prevent overshooting the target and not because different laws of physics apply to German artillery!!!

[syhprum]

For 45° not only must the Earth be flat but it must be infinite in extent.
during WWII about 8 shells coming from the south landed on Maidstone about 65 miles from the nearest German occupied territory apparently 21cm missiles from a K12 they had not lost their enthusiasm for experimenting with long range guns.

[imatfaal]

I would imagine they fired the gun at 55* to prevent overshooting the target and not because different laws of physics apply to German artillery!!!

  Who mentioned different laws of physics?  It could have been
1. that the position they fired from was important - thus to hit Paris rather than overshoot you aim a little suboptimally
2. They calculated/discovered this was optimum and the gun was sited a far from France as possible.
3.  The physical gun was not able to support itself at 45 degrees but was a 55 degrees
Without further evidence any of these or a combo or a different answer entirely could be true

For 45° not only must the Earth be flat but it must be infinite in extent.

  Air Resistance is a far far bigger effect and will always swamp the difference between a parabolic and a elliptical course

during WWII about 8 shells coming from the south landed on Maidstone about 65 miles from the nearest German occupied territory apparently 21cm missiles from a K12 they had not lost their enthusiasm for experimenting with long range guns.

  I didnt know that - glad they didnt manage to get any further northwards, my mum stayed in London all through the war!  The psychological damage was, apparently, the most important effect of the Paris Gun and they already had that with the V1s and later with the V2s in the second world war. 

[syhprum]

There was no was psychological damage in Maidstone as we were just told they were anti aircraft shells that had gone astray but I knew better as at one location you could see where the shell had come thru the branches of a tree on its way but during the war you believed what you were told to believe !!

PS this happened the day before the first V1 came over.

[imatfaal]

There was no was psychological damage in Maidstone as we were just told they were anti aircraft shells that had gone astray but I knew better as at one location you could see where the shell had come thru the branches of a tree on its way but during the war you believed what you were told to believe !!

PS this happened the day before the first V1 came over.

as a personal opinion/memory - which affected you more mentally, in terms of anxiety, worry, and shear terror; the sudden V2s or the dreadful droning warning of the doodle-bug V1s.  My parents are divided; one preferred the V1s as it gave you a few moments to prepare, the other hated the V1 for those very same moments of dread listening for the noise to stop...