Quincy Rotary Screw Sales Manual Useful Formulas
1) Estimating horsepower requirements at pressures other than rated pressure.
In most rotary screw compressors, increasing or decreasing the pressure settings will have
similar effects. The rule of thumb is:
For every I PSIG change from rated pressure, the brake horsepower required will change 0.5% from the rated BHP. Increase the pressure by 10 PSIG and the BHP will go up 5%. Decrease the pressure by 20 PSIG and the BHP will go down 10%.
2) Estimating volume flow rates at pressures other than rated pressure.
Changes in discharge pressure from the rated pressure of the compressor will result in changes in the overall compression ratio. These compression ratio changes will cause changes in the volumetric efficiency of the compressor that will result in changes in capacity. The rule of thumb is:
For every 10 PSIG change from rated discharge pressure, the CFM capacity of the compressor will change 0.4% from the rated capacity. Reducing pressure from 110 PSIG to 100 PSIG will result in a capacity increase offour tenths of one percent. Increasing the pressure by 10 PSIQ will cause a reduction in capacity of about four tenths of one percent.
3) Estimating power costs.
To estimate power costs, you will need to know the following:
 What is the cost per KWH?
 How many hours per year does the compressor run?
 At what capacity will the compressor run or how many hours will the compressor run at various load levels?
 What are the brake horsepower requirements of the compressor at the required load levels?
 What is the motor efficiency?
It is important to use actual CFM requirements to figure the load level of the compressor. Do not base power cost calculations on comments like, “About half the time we run at full load and about half the time we run at 70% of full load.” Full load for one machine may not be the same as full load for another machine. Always determine the exact air requirement in order to provide the customer with a power cost calculation that approximates his situation.
Motor efficiencies vary from horsepower to horsepower and from manufacturer to manufacturer within horsepower ranges. The only way to accurately figure power costs will be to use the motor efficiency number on the nameplate of the actual motor being used.
With the above information in hand annual power costs can be estimated by using the following formulas:
1) kW = BHP x .746 / Motor Efficiency
EXAMPLE – Find the kW of a 100 HP, nominal Efficiency motor running at a 95 HP load.
KW = 95 x .746 / .93 = 76.2
2) Cost per Hour = KWH x Power Cost in $
EXAMPLE – Find the cost per hour to operate the compressor in the above example assuming a cost of 7 cents. Cost Per Hour = 76.2 x 0.07 = $5.334
To find the annual power costs, calculate the cost per hour of operating at the various anticipated load levels and multiply by the anticipated number of hours that the machine will operate at those load levels.
4) Estimating additional capacity required to raise system from one pressure to a higher pressure.
To calculate the additional capacity required you need to know:
 Current CFM capacity (total) of all compressors feeding the system.
 Current System Press (PSIG)
 Desired System Press (PSIG)
 Ambient absolute press (PSIA)
The formula for this calculation is:
(Desired absolute system pressure divided by Current Absolute system Press) times Current CFM Capacity equals Actual Capacity required to achieve desired system pressure.
EXAMPLE:
What is the additional capacity required to maintain a 100 PSIG system pressure at sea level in a system that now operates at 91 PSIG using 500 cfm?
(Desired Pressure / Current Pressure) x Current Capacity
(114.7 / 105.7) x 500 = Actual Capacity Required
1.085 x 500 = 542.5 cfm
5) Estimating BTU heat rejection of aircooled rotary screw air compressors.
Heat transfer in rotary screw compressors is dependent on a number of factors concerning efficiencies of lubricant coolers and aftercoolers and the rate of radiant cooling. The only way to arrive at exact heat rejection rates is to actually test the compressor under anticipated operating conditions. Approximate heat rejection rates of rotary screw compressors in standard plant operating conditions for use in designing heat recovery packages or use in sizing additional plant air conditioning requirements can easily be calculated. The rule of thumb is:
The total BTU’s per minute of heat rejected by a rotary screw air compressor is equal to the brake horsepower being used times 42.41. A 100 BHP compressor would have a total heat load of 4,241 BTU/minute. Of this total about 8% is rejected as radiant heat. Of the remaining 92% about 85% (78.2% of total) is rejected through the lubricant cooler and about 15% (13.8% of total) is rejected through the aftercooler.
Calculating BHP Requirements For Less Than Full Load Operation
Modulating single (All and twostage (Ingerso1lRand) rotary screw compressors:
To calculate the horsepower required to produce an amount of compressed air that is less than the full load capacity of a modulating rotary screw compressor, convert the desired CFM demand level into a percentage of the full load capacity of the compressor. If the demand on a 750 CFM compressor was 600 CFM, the percentage would be 80%. Find the Percent of Capacity in the chart below and note the multiplier next to it. Multiply the drive motor BHP by the number corresponding to the demand percentage. This will give you an estimate of the brake horsepower required to meet the specified air demand.
MODULATING
Percent of Full Load Capacity 
Full Load BHP Multiplier 
Percent of Full Load Capacity 
Full Load BHP Multiplier 
Percent of Full Load Capacity 
Full Load BHP Multiplier 

100%  1  80%  0.9577  60%  0.9033  
99%  0.9981  79%  0.9554  59%  0.9001  
98%  0.9962  78%  0.9529  58%  0.8968  
97%  0.9942  77%  0.9505  57%  0.8935  
96%  0.9923  76%  0.948  56%  0.8902  
95%  0.9903  75%  0.9455  55%  0.8868  
94%  0.9883  74%  0.943  54%  0.8833  
93%  0.9863  73%  0.9404  53%  0.8798  
92%  0.9842  72%  0.9378  52%  0.8762  
91%  0.9821  71%  0.9351  51%  0.8725  
90%  0.98  70%  0.9324  50%  0.8687  
89%  0.9779  69%  0.9297  
88%  0.9758  68%  0.927  
87%  0.9736  67%  0.9242  
86%  0.9714  66%  0.9213  
85%  0.9692  65%  0.91 84  
84%  0.967  64%  0.9155  
83%  0.9647  63%  0.9125  
82%  0.9624  62%  0.9095  
81%  0.9601  61%  0.9064  
If, in the above example, the BHP listed for the 750 CFM compressor was 163, then the BHP required at the 600 CFM level (80% of full load) would be 163 x .9577 or 156.1 BHP.
Variable displacement rotary screw compressors with builtin clearance volume (Turn Valve and Spiral Valve):
To calculate the horsepower required to produce an amount of air that is less than the full capacity of a variable displacement rotary screw compressor with builtin clearance volumes, follow the preceding example to determine the percentage of full load capacity. Then use the following table to determine the BHP consumed at the desired load level.
Percent of Full Load Capacity 
Full Load BHP Multiplier 
Percent of Full Load Capacity 
Full Load BHP Multiplier 
Percent of Full Load Capacity 
Full Load BHP Multiplier 
100%  1  80%  0.8629  60%  0.7448 
98%  0.9853  78%  0.8503  
97%  0.9781  77%  0.844  
96%  0.9709  76%  0.83 79  
95%  0.9638  75%  0.83 17  
94%  0.9567  74%  0.8256  
93%  0.9497  73%  0.8 195  
92%  0.9427  72%  0.8135  
91%  0.9358  71%  0.8076  
90%  0.9289  70%  0.8016  
89%  0.922 1  69%  0.7958  
88%  0.9153  68%  0.7899  
87%  0.9086  67%  0.7841  
86%  0.9019  66%  0.7784  
85%  0.8953  65%  0.7727  
84%  0.8887  64%  0.767  
83%  0.8822  63%  0.7614  
82%  0.8757  62%  0.7558  
81%  0.8693  61%  0.7503 
Variable displacement rotary screw compressors without builtin clearance volume
(PowerSync®):
To calculate the horsepower required to produce an amount of air that is less than the full capacity of a variable displacement rotary screw compressor without builtin clearance volumes, follow the preceding example to determine the percentage of full load capacity. Then use the following table to determine the BHP consumed at the desired load level.
POWER $YNC
Percent of Full Load Capacity 
Full Load BHP Multiplier 
Percent of Full Load Capacity 
Full Load BHP Multiplier 
Percent of Full Load Capacity 
Full Load BHP Multiplier 

100%  1  80%  0.8266  60%  0.683  
99%  0.9905  79%  0.8187  59%  0.6766  
98%  0.9811  78%  0.811  58%  0.6701  
97%  0.9718  77%  0.8033  57%  0.6638  
96%  0.9626  76%  0.7956  56%  0.6575  
95%  0.9535  75%  0.7881  55%  0.6512  
94%  0.9445  74%  0.7806  54%  0.645  
93%  0.9355  73%  0.7732  53%  0.6389  
92%  0.9267  72%  0.7659  52%  0.6328  
91%  0.9179  71%  0.7586  51%  0.6268  
90%  0.9092  70%  0.75 14  50%  0.6209  
89%  0.9006  69%  0.7443  
88%  0.892  68%  0.7372  
87%  0.8836  67%  0.7302  
86%  0.8752  66%  0.7233  
85%  0.8669  65%  0.7164  
84%  0.8587  64%  0.7096  
83%  0.8505  63%  0.7029  
82%  0.8425  62%  0.6962  
81%  0.8345  61%  0.6896  
Twostage rotary screw compressor with variable displacement first stage (Suilair):
To calculate the horsepower required to produce an amount of air that is less than the full capacity of a twostage rotary screw compressor with a variable displacement first stage, follow the preceding example to determine the percentage of full load capacity. Then use the following table to determine the BHP consumed at the desired load level.
Percent of Full Load Capacity 
Full Load BHP Multiplier 
Percent of Full Load Capacity 
Full Load BHP Multiplier 
Percent of Full Load Capacity 
Full Load BHP Multiplier 
100%  1  80%  0.9154  60%  0.8167 
99%  0.996  79%  0.9108  59%  0.8113 
98%  0.992  78%  0.9062  58%  0.8058 
97%  0.988  77%  0.9016  57%  0.8003 
96%  0.984  76%  0.897  56%  0.7947 
95%  0.9799  75%  0.8923  55%  0.789 
94%  0.9758  74%  0.8875  54%  0.7833 
93%  0.9717  73%  0.8828  53%  0.7775 
91%  0.9633  71%  0.8731 
90%  0.9591  70%  0.8682 
89%  0.9549  69%  0.8633 
88%  0.9506  68%  0.8583 
87%  0.9463  67%  0.8532 
86%  0.942  66%  0.8482 
85%  0.9376  65%  0.8431 
84%  0.9333  64%  0.8379 
83%  0.9288  63%  0.8327 
82%  0.9244  62%  0.8274 
81%  0.9199  61%  0.8221 
Useful Formulae
 COMP RPM= motor pulley dia x motor rpm
comp. pulley dia.
 MOTOR PULLEY p. d.= comp pulley dia x comp rpm
motor rpm
 COMP PULLEY p. d.= motor pulley dia x motor rpm
comp rpm
 MOTOR RPM = Comp pulley dia x comp rpm
motor pulley p. d.
 FREE AIR = Piston Displacement x volumetric efficiency
 REQUIRED PISTON DISPLACEMENT= free air
vol. eff.
 PISTON DISP. IN CU. FT. MIN. = Cyl. Bore in IN. x Cyl bore x stroke in IN. x rpm
2200
 CU FT COMPRESSED AIR= Cu. Ft. free Air x 14.7
2200
 CU. FT. Free AIR = cu. Ft. free air x (psig + 14.7)
14.7
 CU FT. Free Air Required to Raise Rec. from 0 Gauge to final Pressure=
vol. of Rec. in cu. Ft. x psig
(atmospheric press) p.s.i.a
 CU. FT of Free Air Req’d to raise Rec from some press. Greater than 0 to a final press.
Vol. Of rec in cu. Ft. x (final psig – initial psig)
(atmospheric press) p.s.i.a.
 Piston Speed in Ft. per Min.= 2 x Stroke (in IN.) x rpm
12
 GALLONS = CU. FT.
.134
 CU. FT. = gallons x .134
 Total Force in Lbs. of Air Cylinder = Area of the Cylinder Dia. X PS I G of
in sq inches air press used
 CFM of Free Air req’d to operate= Vol of Cyl X Cycles (Gage Press + 14.7
Cylinder (Single Acting in cu ft Per Min X (14.7)
 PUMP UPTIME (MIN) = V (tank size in gal ) x (final tank press — initial tank press)
7.48 x atmos. Press. (psia) x pump delivery (cfm)
Piston displacement for multistage compressors — only the low pressure cylinders are considered