Calculating exit velocity of a projectile

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SUMMARY

The forum discussion focuses on calculating the exit velocity of a cylindrical projectile launched from an air cannon. The user has gathered essential parameters including dimensions, volumes, distance, time of flight, air pressure, and launch angle. A suggested method involves using the range equation: range = (v^2 * sin(2 * angle)) / gravity, leading to v = sqrt((range * gravity) / (sin(2 * angle))). However, caution is advised regarding the impact of drag on the projectile's flight, as standard equations assume zero drag, which may lead to significant errors in calculations.

PREREQUISITES
  • Understanding of basic physics concepts such as projectile motion and drag forces.
  • Familiarity with the range equation for projectile motion.
  • Knowledge of air pressure effects on projectile dynamics.
  • Ability to perform calculations involving trigonometric functions and square roots.
NEXT STEPS
  • Research the effects of drag on projectile motion, specifically in relation to cylindrical projectiles.
  • Learn about advanced projectile motion equations that account for drag forces.
  • Explore methods for measuring exit velocity using alternative techniques, such as high-speed cameras.
  • Investigate the principles of air cannon design and optimization for improved projectile performance.
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This discussion is beneficial for physics students, experimental researchers, and hobbyists interested in projectile dynamics and air cannon experiments.

zkyzcArn
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I did an experiment using an air cannon to find the drag exhibited on a cylindrical projectile using different mass/density and pressure/velocity. However, I was not able to obtain light gates at the time, so now I have no measurement for velocity. This is necessary for my results, and I was wondering if anyone could help me in calculating it. I have all dimensions and volumes of the components to the air cannon and projectile, distance and time of flight of the projectile, air pressure within the gas chamber and launch angle. If anyone could help me calculate the exit velocity of the projectile it would be greatly appreciated.
 
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im assuming when you say distance that's the range the projectile has gone? if so and you also have the angle then you can use the basic range equation to find the intial velocity.

range = ((v^2)(sin (2*angle)))/gravity
so
v=sqrt((range*gravity)/(sin(2*angle)))

sorry if i read your question wrong but I am in a rush also if my equation doesn't look to neat just search for range equation on google
 
By drag, I assume you mean within the cannon itself as opposed to flight drag of the projectile after it exits the cannon. Be careful about using the standard projectile equations to calculate exit velocity based on range and angle. They assume zero drag during flight. Since flight drag is proportional to velocity (or velocity squared I don't remember), you could be introducing unacceptable error into your calcs. Flight drag may nor may not be an actual issue in your case, but you should be aware of it.
 

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