How do I measure the initial velocity of an object when it is launched and air resistance is taken into account???

Update:

sorry, please IGNORE the first question...

I'm doing a practical involving projectile motion:

"Do shapes, weight and density affect the range of the projectiled objects?"

I've been doing research for weeks trying to figure out how and what to use to launch these objects (all objects being launched with the same velocity). Plus, with the presence of air resistance finding the final velocity, i think, is hard...

Relevance
• pete m
Lv 4

Your not being entirely clear with your question, Initial velocity of a launching object is 0 m/s to measure acceleration you will need to track the object over a known distance or measure the distance after a certain time for a number of occasions, (speed or velocity = distance/time). acceleration is given as distance/unit time/unit time (yest you need both unit times) Resistance due to air is a measure of a number of things friction and aerodynamics. Terminal velocity is the maximum velocity an object can reach during free fall, which for a human is of the order of 100 miles/hour

Acceleration of free fall due to gravity is given as 10m/s/s in other words after 1 second the object is travelling at 10m/s after 2 seconds 20m/s and so on.

In terms of rocketry you will need to reach escape velocity ie enough velocity to pull free of the gravitational pull of the earth.

I'm going to add you to my watch list if you have more info about what you are trying to achieve I will see if I can help but it has been a long time since I did any of this....

In real life, shape and density will effect the range of a projectile. This is why bullets are made of streamlined lead and not feathers!!

I had to construct a projectile motion launch device about 14 years ago and found it nigh on impossible to accurately determine air resistance with the resources I had to hand so I created a crossbow launcher from a kids toy and used a dart.

You could crank back the launcher to differnt distances to alter the initial velocity.

To calibrate it I simply cheated. I set the angle at 45deg and found how far the dart went for each shot (dart sticks into a wooden bench quite nicely at 45 deg) and empirically worked out what the launch speed was from the range.

(I made some nerdy waffle about 1/2kx^2 = 1/mv^2 in the write up but I never really solved it that way. Too much like hard work and the answer would have been wrong anyway as elastic, erm, ins't elastic)

If in doubt, cheat.

• Anonymous

for any projectile, consider it moving in the x-y plane. as the object moves through y, it is subjected to two forces, gravity and air resistance. ie: the sum of the forces in the y direction are F= mg+f=ma, where g=9.81m/s^2, f is the force of friction that is air resistance, and m is the mass of the object. now look at the forces in the x direction, where there is no g: F=f=ma, where a is now the acceleration due to air resistance. This f (which is the same in the x and y directions) causes an acceleration to m in both x and y. f will vary for different objects, through different media. If air is the media in question, then it will be the same for all objects, but the shape of the object, as well as the size will effect what the value of f is.

If acceleration is high, the initial or launch velocity should be very close to the drag-free value since there's been so little time to lose energy to drag. OK, you say ignore the question but I'll leave the answer.

Air resistance is very significant for any kind of rocket. Smaller rockets (e.g., "model" rockets) don't go very fast but they are light, and larger more massive rockets go much faster. Either way, this means a large drag decelerative term. The basic drag equation is Fd = k * air density * v^2 * frontal area * drag coefficient. (Don't you love that "k"? Sometimes it means "I may have forgotten a term" but in this case I've covered them all, and k simply = 1/2.) The cumulative effects of drag can be huge due to increasing speed and decreasing mass (and thus decreasing "ballistic coefficient", which is resistance to drag, defined as mass/frontal area), especially in flatter trajectories where the air density stays high contrasted with go-to-orbit trajectories. Since velocity and altitude (and therefore air density) are continously varying in a rocket flight, trajectory analysis would be at best very approximate if attempted with a closed-form (analytical) formula and is better handled with a high fidelity simulation. But even a lower fidelity one, say with rough solutions taken over several points in the flight, can be useful for initial sizing/design analysis.

• Steve
Lv 7

To get back to your actual ?, you are trying to establish the effect on range of shape, weight and density of a projectile when air resistance is taken into account:

Shape: Very important. The more streamlined, the greater the range.

Weight: Almost no importance. Weight is simply a reflection of the size of the projectile.

Density: Very important. Greater density = greater range. Think of why bullets are made of lead or other dense materials.

Source(s): Aero engineer, ret.
• Anonymous

The air resistance is considered to be proportional to the square of the velocity..

f = -(1/2)CpAv^2

Where p = air density, A= cross-sectional area, C= drag coefficient. C is 0.5 for spheres, and is about 2.0 for irregularly shaped objects.

F_x=-K_xmv_x^2

While the projectile is moving upwards...

F_z=-mg-K_zmv_z^2

and downwards...

F_z=-mg+K_zmv_z^2

Where I have used two different K's, because I figure that the cross-sectional areas in the yz and xy plane would be different. They would be the same if a sphere, however.

Source(s): http://hyperphysics.phy-astr.gsu.edu/hbase/airfri2... Serway, Raymond, Physics for Scientists and Engineers,with Modern Physics, 3rd Ed, Saunders College Publishing, 1990.

Actually Pete M, according to my brain and my teacher initial velocity is the speed of the projectile. It is only 0 m/s when the projectile is at it's ighest point.

But to answer the question, use the suvat equations to work out the velocity of the object.

Source(s): my brain and teacher
• Emil
Lv 5

A Laser Doppler Velocimeter can be used for Measuring the Initial Velocity of a Projectile.

http://stinet.dtic.mil/oai/oai?&verb=getRecord&met...

Corporate Author : NAVAL ACADEMY ANNAPOLIS MD

Resistance in the air really depends on the shape of your projectile hence its CX (coefficient of penetration in the air).