How do you calculate G- force?

Question

I'm doing a science fair project growing plants in some G-Force. They will be spinning at a constant rate on a disc. How do I calculate the G-force that is being applied? Thanks!

Answer 1

F = mv^2/r = ma; where F = centripetal/centrifugal force, a = centripetal acceleration, m = mass of your plants, v = wr = tangential velocity of your plants spinning around at a radius = r distance from the center of the spin. w = angular velocity in radians [See source.] per second, which is just how fast you are spinning the plants.

G = a/g; where a = F/m = v^2/r from the earlier equation. In other words, a G is just the equivalent number of g = constant = 9.81 m/sec^2 or 32.2 ft/sec^2 at Earth's surface in the centripetal acceleration (a) generated by spinning the plants.

Combining equations above, we have G = v^2/rg = (wr)^2/rg = (w^2)r/g; where g = 9.81 m/sec^2 if r is measured in meters or = 32.2 ft/sec^2 if r is in feet.

SUGGESTION: You have the makings of a good science project. But to make it even better, divide your plants (seeds) into two or more groups: one or more test groups and a control group.

Do your G thing at different G levels, one level for each of the test groups, but let the control group develop without G's. Make sure all other things on the groups are the same (e.g., water, soil, temperature, sunlight); so that the only difference between the test and control groups are the G's.

Then, after the plants have grown, take data from all groups to see if there are significant differences in weight, number grown (starting with the same number of seeds), height and width, number of flowers (if applicable), and so on. If you do this, then you could make some insightful conclusions about the effects of G's on your plants.

This could be a great, prize winning project. Have fun.

Answer 2

What you are trying to calculate is centripetal acceleration.

The formula is a=v^2/r where v is the velocity in feet per second, and r is the radius in feet. The velocity will be in feet per second per second.

To get the velocity of a point on a spinning disk, take v = 2 * r * pi * rpm / 60
Where r is the distance from the disk's center, pi=3.14159, and rpm is the number of revolutions per minute.

Once you have the acceleration, you can convert it to G by dividing by
32.174 feet per second per second.

An example: Lets say you have a disk 6 feet in diameter, and you are spinning it at 40 rpm.:
v = 2 * r * pi * rpm / 60
v = 2 * 3 feet * 3.14159 * 40 / 60 seconds
v = 12.57 feet per second
The velocity at the edge is 12.57 feet per second.


The acceleration would be:
a = v^2 / r (that is v squared divided by r)
a = 12.57 * 12.57 / 3 feet
a = 52.67 feet per second per second
g = 52.67 / 32.174 ( we divide here by the value of 1G=32.174 ft/s/s)
g = 1.64 G.

However, this is the acceleration away from the center of rotation. Your plants are also affected by the 1 G of the Earth's gravity. Since the two forces are perpindicular to each other you can't just add them. You calculate the total effective 'gravitational' force like this:

total_g = sqr( earth_g^2 + spin_g^2 ) (sqr means take the square root)

so if earth_g is 1 and spin_g is 1.64:
total_g = sqr ( 1^2 + 1.64^2 )
total_g = sqr ( 3.6896 )
total_g = 1.92 G

Your plants weigh almost double their normal weight at the edge of a 6 foot disk spinning at 40 rpm!

Hope this helps.

Answer 3

You need to test with a person.
Start your mechanism...When you hit your constant speed, count how many "Gees" the person says...
For example, I make a quick turn with my car...My passenger says, "Oh, gees...Oh, gees"...
I have concluded that I pulled 2 G's.