Explanation of how the design works
The design consists of two two-stage reciprocating air compressors. The key aspect of our
design is the utilization of both ends of the drive shaft that is driven by the motor. For our
design, two pistons, mounted opposite of each other, are driven by the same cam wheel which is
mounted to one end of the drive shaft. Mounting the pistons parallel and opposite to each other
ensures that the stroke of the pistons will be in sync, so that the minimum volume of one piston
occurs at the maximum volume of the other. The pistons are designed to travel the same distance
in each cylinder. However, one cylinder has a greater diameter than the other. This difference in
diameter, and therefore volume, enables the two stage compressor to achieve the desired
compression ratio of 10 to 1. Because there are two pistons, the total compression ratio is the
product of the compression ratio of each stage. To achieve a 10 to 1 ratio, the ratio of each stage
is designed to be 3.6 to 1. All dimensions of our preliminary design can be found in the
schematic diagram.
The compression process is like this. Air is taken into the first piston. The piston then
compresses this air until the volume of the first piston is zero. This ensures that all of the air is
compressed into the second piston, which at this point will be opened to its maximum volume.
At this point the air in the second piston should be at 3.6 times atmospheric pressure. Once the
air has been fully compressed into the second piston, the second piston compresses to a ratio of
3.6, putting the air at an overall pressure of 10 times atmospheric. At this point, the cycle repeats
itself. Our design incorporates one way valves between each piston.
The driving force behind the pistons consists of two rods connected at the same point to the
circular cam. The cam turns at a constant speed, driving the pistons. The diameter of the cam is
equivalent to the distance of travel of each piston. Our design is made up of two two-stage
compressors, so four pistons in all. For the flow-rate test, the two sets of pistons will be
connected to the same output hose. For the pressure test, one set of pistons will simply be
disconnected and the pressure will be taken with one set of pistons. This should reduce the
possibility of leakage.
Calculations
When dimensioning the air compressor, the first thing decided on was the maximum final
pressure achievable. Based on research and results from previous years’ competitions, a goal
pressure of 150 PSI was decided. Knowing that atmospheric pressure is approximately 14.7 PSI,
a compression ratio needed to reach our goal could be calculated. To calculate the volumetric
ratios of the two compression stages, the following equations are used:
2
Vcyl1  lt1   ri1
Vcyl2 
V3 
Vcyl1
(1)
(2)
CR
Vcyl2
CR
where Vcyl1 is the initial volume of the first cylinder, Vcyl2 is the volume of the first cylinder
compressed plus the second cylinder expanded (or in this case, just the volume of the first
(3)
cylinder expanded because the first cylinder’s volume is 0 when compressing), V3 is the
compressed volume of the second cylinder, lt1 is the length of travel of the first piston, ri1 is the
radius of the first piston, and CR is the compression ratio.
Now that the volumetric ratios are figured out, design of the cylinders’ diameters and
depth can be considered. A function designating the length of the second piston can be made
using Vcyl2 and the radius of the second cylinder:
ltotal2 
Vcyl2
 2
 ri2
(4)
where ltotal2 is the length of the second cylinder and ri2 is the radius of the second cylinder. A
function is also created to designate the position of the piston at cylinder two’s compressed state:
lt2 
V3
(5)
 2
 ri2
where lt2 is the distance from the cap of the cylinder from the piston during cylinder two’s
compressed state. Using ltotal2 and lt2, we can easily find the distance traveled by the piston in the
second cylinder by taking the difference of the two. This distance will be denoted by variable
ltravel2.
Since the pistons’ travel distances, cylinder radii, and cylinder lengths are all related,
functions for the pistons’ driving rods’ minimum length can now be calculated by using the
equation
2
l 
ri1  trod   t12   lt1
(6)
     t 
lrod1 
rod
ri1  trod
 2

where lrod1 is the minimum length that cylinder one’s piston’s driving rod can be so that it does
not hit the sides of the cylinder and trod is the thickness of the driving rod. The same can be done
for cylinder two by using its respective values.
2