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:

  1.  What is the cost per KWH?
  2.  How many hours per year does the compressor run?
  3.  At what capacity will the compressor run or how many hours will the compressor run at various load levels?
  4.  What are the brake horsepower requirements of the compressor at the required load levels?
  5. 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:

  1. Current CFM capacity (total) of all compressors feeding the system.
  2. Current System Press (PSIG)
  3. Desired System Press (PSIG)
  4. 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 air-cooled 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 two-stage (Ingerso1l-Rand) 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 built-in 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 built-in 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 built-in 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 built-in 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

 

Two-stage 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 two-stage 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

 

  1. COMP RPM= motor pulley dia x motor rpm
                                 comp. pulley dia.

 

  1. MOTOR PULLEY p. d.= comp pulley dia x comp rpm
                                                     motor rpm

 

  1. COMP PULLEY p. d.= motor pulley dia x motor rpm
                                                     comp rpm

 

 

  1. MOTOR RPM = Comp pulley dia x comp rpm
                                     motor pulley p. d.

 

  1. FREE AIR = Piston Displacement x volumetric efficiency

 

 

  1. REQUIRED PISTON DISPLACEMENT= free air
                                                                  vol. eff.

 

 

  1. PISTON DISP. IN CU. FT. MIN. = Cyl. Bore in IN. x Cyl bore x stroke in IN. x rpm
                                                                                   2200

 

  1. CU FT COMPRESSED AIR= Cu. Ft. free Air x 14.7
                                                            2200

 

  1. CU. FT. Free AIR =   cu. Ft. free air x (psig + 14.7)
                                                      14.7

 

  1. 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

 

  1. 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.

 

  1. Piston Speed in Ft. per Min.= 2 x Stroke (in IN.) x rpm
                                                                  12

 

  1. GALLONS = CU. FT.
                          .134

 

  1. CU. FT. = gallons x .134

 

  1. Total Force in Lbs. of Air Cylinder =  Area of the Cylinder Dia.  X  PS I G of
    in sq inches                          air press used

 

  1. 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)

 

 

  1. 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 multi-stage compressors only the low pressure cylinders are considered