by Tdarcos » Mon Dec 20, 2021 6:09 am
I believe the term you're looking for is "slope-intercept form." It's used in the calculation of ballistic trajectories, which is what you need when firing (or aiming) one moving thing (projectile) at another moving thing (target). You're trying to discover the straight line from where you are firing that gets the projectile to the destination where the target will be at when the projectile will arrive.
Because the distance and speed determine where the projectile will be at any specific time, the same calculation has to be made for the target. You connect how far it can move then you adjust how far in front of the target you aim to hit it on arrival.
Let's take an example, you're an assassin, trying to shoot a politician on a parade float. The float will move at 5 mph, or 7.333(repeating) feet per second. Your rifle fires a bullet at 1200 fps. If you're 300 yards away, or 900 feet, the bullet will take 9/12 of one second to arrive, or 0.75 seconds, so the target will move 5.4 feet in the time it takes for the bullet to travel 900 ft. Well, if you aim straight at him, you'll miss his head by that much. So you need to know what tiny amount of movement of the rifle left compensates for the difference in distance. At this distance the extra time for the bullet to travel the increased distance diagonally is negligible, but if you're firing a 30" naval gun at a plane moving at 300 mph, you have to compensate for that, too; These are the things the slope-intercept calculations tell you.
In fact, calculating ballistic trajectories is the reason we have computers today. The government funded research on machines that could do ballistics. Computers came from that need.
I believe the term you're looking for is "slope-intercept form." It's used in the calculation of ballistic trajectories, which is what you need when firing (or aiming) one moving thing (projectile) at another moving thing (target). You're trying to discover the straight line from where you are firing that gets the projectile to the destination where the target will be at when the projectile will arrive.
Because the distance and speed determine where the projectile will be at any specific time, the same calculation has to be made for the target. You connect how far it can move then you adjust how far in front of the target you aim to hit it on arrival.
Let's take an example, you're an assassin, trying to shoot a politician on a parade float. The float will move at 5 mph, or 7.333(repeating) feet per second. Your rifle fires a bullet at 1200 fps. If you're 300 yards away, or 900 feet, the bullet will take 9/12 of one second to arrive, or 0.75 seconds, so the target will move 5.4 feet in the time it takes for the bullet to travel 900 ft. Well, if you aim straight at him, you'll miss his head by that much. So you need to know what tiny amount of movement of the rifle left compensates for the difference in distance. At this distance the extra time for the bullet to travel the increased distance diagonally is negligible, but if you're firing a 30" naval gun at a plane moving at 300 mph, you have to compensate for that, too; These are the things the slope-intercept calculations tell you.
In fact, calculating ballistic trajectories is the reason we have computers today. The government funded research on machines that could do ballistics. Computers came from that need.