Imagine an isosceles triangle named ABC. It may be helpful to draw this on a piece of paper to understand.

Point A is your projectile's starting point.
Point B is the projectile's Apogee
Point C is the target.

-Segment AB and BC are the legs of the Iscosceles Triangle (sides that are equal)
-Segment BC is the base (unequal side).
-The Length of Segment AB represents the range of the projectile BEFORE it reaches its apogee (rocket fires 1000 ft before it reaches it's apogee, then AB = 1000 ft.)
-Segment BC is the ground; nothing more.

To aim accurately, you need to make sure the projectile's apogee is halfway between Point A and Point C. (Halfway between the starting point, and the target)

So, if you need to hit a target 50m away with a shell that shoots 100m BEFORE it reaches its apogee, you will need to shoot it at a steeper angle to ensure that it lands in the right place...unless you fire it straight at the target.

If you need to hit a target 150m away with the same shell that shoots 100m...you will have to fire at a lower angle.

If the target is 200m away or more, you can't hit it. Hinge Theorem says "the length of 2 sides of a triangle added together MUST be LONGER (not equal to) the third side." In practical terms, angle BAC will be 0 degrees. You will be shooting straight at the target, and the shell will be 100m short.

As a general rule: If the distance to the target is SHORTER than the range of your weapon, the greater the measurement of angle BAC (the taller the triangle); If the distance to the target is LONGER than the range of your weapon, the lower the measurement of angle BAC (the flatter the triangle)...up until the target's distance is twice the range of your weapon.

To find the specific measurement of angle BAC, it may help to draw a scale model of this triangle on a piece of paper, and measure the angle with a protractor.

None of this is counting wind or other weather conditions that may arise.


[This message has been edited by TariqMujahid (edited 03-11-2002).]

I entirely fail to see how that will help you aim at anything. That doesn't copensate for windage, gravity, or curvature at all, which is what trips most people up. If I'm missing something here feel free to correct me, but I can't make out what that's supposed to do for you.

~Zero the Inestimable

Surely you didn't think this was a direct representation of the projectile's flight...This is a way to determine what angles will hit objects at what distances. I didn't include the wind or other weather factors. I also know i wasn't very specific when i wrote this..."Higher Angle" "Lower Angle". I will fix this.

I don't know what curvature is- is that how wide the curve is connecting the object's ascent and descent? If that's what it is, then it is included...the maximum height in that curve would be point B.

What do you mean by gravity? Do you simply mean the force that makes things fall? If that's the case, i assume you aren't understand why segment BC is falling at an angle instead of straight down. This is simple: If something goes up at an angle, it falls at that same angle. I don't know why this is (i'm still in 9th grade, i have not gotten into physics), but i assume it has something to do with the object's momentum. This is why the flight path, in a crude form, is an Isosceles Triangle.

This is hard to explain in words, maybe i'll draw a picture and post it.

Thankyou for the criticism, i will use your suggestions to make this better.

[This message has been edited by TariqMujahid (edited 03-11-2002).]

A bullet in flight does not follow a perfect arc. It's flight depends on how fast it decelerates, which is determined by a multitude of factors.

Visual aid:

code:

---

Real
         ____
_�_---����    ��-_

Theoretical

__�_----����----__�_    

---

You getting the picture now? You'd have to move the point of your triangle up or downrange depending on the circumstances.

~Zero the Inestimable

I agree with Zero.

In theory it all sounds well and good, but ballistics is alot more complicated than that.

Curvature absolutely has an impact on the "projectile", whether from a direct fire or indirect fire delivery system. The aerodynamic design of said projectile plays a large role, followed by method of propulsion, gravity, and drag (atmospheric friction).

In a vacuum, with a gravitational constant, your theory would be spot on. But within the restraints of earths atmosphere, the projectile decelerates because of the drag against it and eventually drops like a rock, and in no way will it mirror the path of the projectile prior to apogee. There will still be some forward momentum, yes, but not in any way that can be exactly quantified and measured (unless you're a true physics guru with more mathematics under the belt than I'll ever have).

The ability to predict projectile paths (being able to plot the course and target) comes almost mainly from sending alot of rounds downrange using different KNOWN variables to see how things change. That's how come the good reloading books are so freaking big, and why arty personnel have plotting books. Still, it's not an exact science and some variables aren't constant (like wind speed & direction), hence the use of spotters and forward observers when it really matters.

I see what you all are saying now... I asked a physics teacher in school today; telling him i was trying to predict the shot of a potato gun.

Using my above method, you will overshoot every shot. If you have a very aerodynamic projectile, you will overshoot by less.

There will be a range of error, depending on the amount of Air resistance...which is calculated by the following formula:

1/2(ro)V^2*A
RO is the greek letter "ro", which represents Air Density.
V is the starting Velocity of the projectile.
A is the area of the object facing forward.

Hmm...i will have to think up a new way to aim which counts in these factors.

<<<<<.....telling him i was trying to predict the shot of a potato gun.....>>>>>

Hmmm....

If you're doing this for a combustion shooter then I would say you're about to embark on an exercise in futility. You're never garaunteed to use the same amount of propellent for every shot (even if you count), so your results (velocity) won't be consistent. Mind, however, that this is strictly my own opinion.

It WOULD be a practical exercise if you're using a pneumatic though, because you can regulate it to fire off using the same psi every time. You would then only have to pay attention to the weight and "front-end" shape of your spud/projectile. With those variables taken care of your tests will yield more consistent results.

When you have done your tests I would be most interested to hear what happened.

I'm going to make the generic potato gun, with a few modifications... i've addressed this problem of unequal amounts of propellant: i'm going to use a small propaine canister...should that be more consistent? I also plan to drill holes along hte pipe, atleast at the muzzle. This way, the hot gasses go out the sides (making it look cooler) as the soda can (i will use a soda can, it's easier) goes out the front.