I’ve often wondered why drag race cars don’t use pneumatic rams to give them a boost of initial acceleration. The system would work on the same principles as an aircraft catapult. You could set up the ram to push against a rubber pad that you set on the ground, pushing you forward. Or you could set up a block on the ground, similar to starting blocks that Olympic runners push against at the start.
The pneumatic ram could be supplied by a scuba tank (also called a diving cylinder). A scuba tank holds 12 liters air at 3000 psi. That’s over a million joules (1 megajoule) of energy! For comparison, a gallon of gasoline contains 120 megajoules of energy, so releasing the air of a diving cylinder is equivalent to burning 1 fluid ounce of gasoline. The difference, however, is the scuba tank can release all of its energy at once, while the gasoline would have to be burned by an engine. When a Bugatti Veyron’s 1,001 horsepower engine is running full-out it uses 1.4 gallons of gasoline per minute. That’s 3 ounces of gasoline per second or 1 ounce every 1/3 of a second. A diving cylendar could certainly release all of it’s energy in 1/3 of a second, matching the Bugatti Veyron’s massive engine horsepower with far less weight.
A 3000 psi diving cylinder may be able to deliver 20,000 kilopascals of pressure to a pneumatic ram. You could take all of that pressure and put it into a pneumatic ram. An air cylinder with a 80mm bore diameter would deliver about 100,000 newtons of force. That same 80mm bore pneumatic ram has a stroke of 300mm. So how fast would a 1000 kg car be traveling from this one ram pushing on it from a dead stop?
To find acceleration when we know mass and force we can use Newton’s second law of motion:
- m = mass = 1,000 kg
- F = force = 100,000 N
- Newton’s second law of motion is F = m*a
- ∴ a = F/m = 100,000/1,000 = 100 m/s^2
For comparison, a Bugatti Veyron Supersport can acclerate from 0-60 MPH in 2.46 seconds. Since 1 MPH = 0.44704 meters per second, the Bugatti acclerates to 26.8224 m/s. Since Acceleration = change in speed ÷ time interval, the acceleration of the Bugatti is 26.8224/2.46 = 10.9 m/s^2.
To find the final velocity (instantaneous velocity) when we know distance and acceleration we can use Torricelli’s equation:
- Torricelli’s equation: Vf^2 = Vi^2 + 2aΔd
- ∴ Vf = sqrt(Vi^2 + 2aΔd)
- vf = final velocity (what we want to know)
- vi = initial velocity = 0
- d = distance = 0.3 meters (the stroke of the ram)
- a = acceleration = 100 m/s^2
- Vf = sqrt(Vi^2 + 2aΔd)
- Vf = sqrt(2*100*0.3) = 7.75 meters per second
- 1 meter per second = 2.23694 miles per hour
- Vf = sqrt(2*100*0.3)*2.23694 = 17.3 MPH
So a pneumatic ram could a accelerate a 1,000 kg car to 17 MPH over a distance of just 1 foot!
What if we used 10 rams? Would we be going 170 MPH?
- Ten 100,000 newton rams = 1,000,000 newtons (1 meganewton!)
- a = F/m = 1,000,000/1,000 = 1,000 m/s^2
- Vf = sqrt(2*1000*0.3)*2.23694 = 54.8 MPH
So if you used pneumatic power to create 1 meganewton of force, you could accelerate a 1,000 kg car to almost 60 MPH in just 1 foot!