altitude ?

[agent141]

was wondering if there was a formula to estimate altitude, if angle of departure and distance traveled and projectile weight are known quantities ??

[Double D]

I think you are going to have know a few other things also, like  velocity and time of travel...CW an old Cannon cocker like yourself should be right on top of this.

[Rickk]

There is a simplistic formula that I made an excel spreadsheet out of. It assumes no wind drag loss which, for heavy projectiles and slower velocities is not a major source of error.

You need to know the angle of launch and only one of the following to figure it all out... time of flight, distance traveled, or muzzle velocity.

I just searched my home computer for the spreadsheet... can't find it. It may be on my computer at work. I will check Monday and see if I can find it.

The calculation involves splitting the velocity up into horizontal and vertical velocities. At the muzzle, the horizontal velocity is the muzzle velocity times the cosine of the angle. The vertical velocity is the muzzle velocity times the sine of the angle.

I ignored wind resistance, so the two velocities do not change due to wind resistance. The horizontal velocity therefore remains constant thru the entire flight. The vertical velocity is equal to the original velocity minus the velocity that things fall at do to gravity. In the spreadsheet, I calculated at 1/10th second intervals. Each calculation takes the previous vertical velocity and subtracts negative acceleration due to gravity from it to calculate a new vertical velocity. It also keeps a running total of the vertical height. The height and distance can be plotted on a graph  to see the flight path.

[agent141]

great , I do know the exact angle and distance 70deg / 400yd / 16lb by the way, made a hell of a crash in the woods when it came down on an old tree.

[Cat Whisperer]

Agent141 -

WELCOME to the board!

My ISP has been down for FOUR DAYS - serious withdrawal symptoms here.

With modern artillery one calculates from tables to find the correct charge and elevation from knowing:

elevation of cannon (above sea level)
elevation of target
direction and velocity of wind at each 500 foot level above the deck
powder temperature
exact weight of the projectile
direction of fire (to crank in the rotation of the earth)

The formulas have all been worked out to give azimuth and elevation (angle of) for the guns using a specific charge (1 through 7) of green bag or white bag powder.  Time of flight is also reported (useful for doing an airburst with a time-setable fuse).

The path of flight is roughly a parabola.  The bullet is slowing down constantly, and the pitch of the bullet is aligned with the path of the bullet only during the first third or so of the flight - from there nose is elevated some, which affects the flight characteristics.  Drift to the right from rotation of the projo is also accounted for. These are different when using a sphere or other shape.

SO, height is a varialbe mostly of velocity and angle of elevation, other factors modifying it a bit.  You could make some ROUGH estimates of velocity by guessing that time going up is about equal to time comming down and that deceleration upward is wind friction and acceleration of gravity (and time falling related to acceleration of gravity less wind friction).

OR, you could make several observations from known points at a known time of the angles and distances involved - much as a forrester would use triangulation to determine the height of trees without climbing them.

I considered asking the folks at the airport about getting a radar tracking when I fired my 4.5" mortar for the first time (because the machine shop where it was made was next to the airport); but I didn't know an ATC well enough to ask.

[Cat Whisperer]

Altitudes are calculated at various points in the path, so when one uses a VT (variable time) fuse one knows whether it will clear an obstical (like a mountain or radio antenna) with out setting off the fuse (which works by sending out a signal and listening for the return of the signal - when it's reflected from something and is received strongly enough the round goes off).

[m223]

Agent141, sorry I'm no help with your question, but I will give you a great big welcome to the board. The people here are great.   Tracy  (m223)

[agent141]

Rickk .. any luck finding that formula?