Womack Data Sheet 47: Tips on Sizing Accumulators
Space does not permit a full discussion of accumulators, and this issue will be limited to a practical method of determining the minimum capacity of an accumulator when used to supplement the flow of oil from a pump as in the circuit shown below.
In the basic circuit a closed center 4way valve is used. The purpose of the accumulator is to store high pressure oil from the pump during periods when the 4way valve is centered. When stored pressure reaches a predetermined maximum (usually 3,000 PSI) the pump is automatically unloaded and allowed to idle for the remainder of the cycle. Either a special pilotoperated unloading valve or a pressure switch and solenoid dump valve is used. When the 4way valve is shifted to start the cylinder, the stored oil adds to the pump flow to give the cylinder a speed greater than from pump oil alone.
The big advantage of accumulators on this type system is that a smaller (and less expensive) pump, electric motor, and control valve will do the same job as larger and more costly components. See rule of thumb on percentage duty cycle.
Additional information, plus many accumulator circuits are shown in publications by Womack Machine Supply Co., including "Industrial Fluid Power  Volume 1", and "Fluid Power in Plant and Field".
System PSI. Optimum system pressure for most accumulators is 3,000 PSI. They have maximum energy storage at least cost and smallest size when operated at their maximum pressure rating. Although 5,000 PSI models are available in some brands, their greatly increased cost offsets their pressure advantage, so they are less desirable on most systems.
Compressibility. An accumulator adds compressibility in the oil stream between pump and 4way valve, and if this is undesirable an accumulator should not be used. However, on systems using a pressure compensated flow control valve or a servotype 4way valve, compressibility in the line ahead of the 4way valve is not usually objectionable.
Basic accumulator circuit in which a low volume pump stores high pressure oil in the accumulator
while the 4way valve is centered. Pump oil plus accumulator discharge gives cylinder a rapid stroke.

Minimum 
Maximum System PSI With Accumulator Fully Charged  
3,000  2,750  2,500  2,250  2,000  
2,700  12                     
2,600  17                     
2,500  22  11                
2,400  27  16                
2,300  33  21  10           
2,200  40  27  15           
2,100  46  34  21  8      
2,000  55  41  27  14      
1,900  63  49  35  20  6 
1,800  73  58  43  27  12 
1,700  84  67  51  35  19 
1,600  96  79  61  44  27 
1,500  109  91  73  55  36 
1,400       105  86  66  47 
1,300            101  80  59 
1,200  Cubic inches of oil discharged from a "1" gallon accumulator. 
96  73  
1,100       89 
Figures in the body of the chart are the number of cubic inches of oil which can be discharged from a "1gallon" accumulator, starting with a fully charged pressure shown along the top of the chart and discharging until the system pressure falls to values shown in the left column. With larger accumulators, multiply the figures in the chart times the gallon capacity of the accumulator. For example, if working with a 10gallon accumulator, multiply chart figures times 10, etc.
Figures in the chart are about 5% less than if calculated by Boyle's Law for theoretical discharge. This is to compensate for loss of capacity during discharge caused by a temperature drop in the gas when the accumulator is discharged rapidly.
For operating conditions beyond the range of the chart, the formula in the box below may be used. As explained in the text, accumulator systems are most often designed for a fully charged accumulator pressure of 3,000 PSI.
How to Use the Chart
As oil is allowed to discharge from a piston or bladder type accumulator, the pressure of the oil drops. For example, looking at the chart above, in the 3,000 PSI column, when 12 cubic inches of oil are discharged from a 1gallon size accumulator, the pressure falls from 3,000 to 2,750 PSI, etc. So, one important factor in arriving at an adequate size accumulator is to select a size large enough so this inevitable drop in pressure will not affect normal operation of the hydraulic circuit. Cylinders and hydraulic motors must be large enough to produce the required force or torque at the final pressure remaining at the end of accumulator discharge. In finding the "gallon" capacity needed in a particular application, follow these design steps:
Step 1. Calculate or estimate as accurately as you can, the volume of oil, in cubic inches, which will be needed from the accumulator on each discharge cycle, to supplement the volume of oil flowing from the system pump.
Step 2. Considering the size of cylinders or hydraulic motors being used, calculate to what level the pressure can drop during the discharge cycle without the output force or torque falling below an acceptable level.
Step 3. In the chart, use the column headed by your system pressure when the accumulator is fully charged. In the left column find the lowest acceptable system pressure at the end of the discharge cycle. The figure in the chart is the number of cubic inches of oil which can be recovered from a 1gallon size accumulator under these pressure conditions.
Example: If your fully charged pressure is 3,000 PSI, and your lowest acceptable pressure is 2,000 PSI, the chart shows that 55 cubic inches can be recovered from a 1gallon accumulator. Suppose you calculated that 230 cubic inches will be needed for your application. The minimum accumulator capacity is: 230 ÷ 55 = 4.18 gallons. The nearest standard accumulator size is 5 gallons  the correct size to use.
While figures in the chart show 5% less volume than calculated, to take care of loss of capacity which occurs on a quick discharge, the accumulator, when used on long holding applications, will eventually give back an additional 5% of oil as the shell, slightly cooled by the quick discharge, gradually warms back up to normal temperature.
Mathematical Solution for Accumulator Size
The following is a general formula which will solve for the cubic inch oil discharge from any size accumulator under any conditions of precharge and system pressure. It may be used for operating conditions not covered by the chart.
A lossofcapacity allowance of 5% is built into the formula to take care of loss of capacity caused by temperature changes as the gas compresses and expands.
D = [0.95 × P1 × V1 ÷ P2]  [0.95 × P1 × V1 ÷ P3]
D is the number of cubic inches of oil discharge.
P1 is the nitrogen precharge pressure, in PSI.
P2 is system pressure, in PSI, after volume D cubic inches has been discharged.
P3 is maximum system pressure, in PSI, with accumulator fully charged.
V1 is the catalograted gas volume of the accumulator, in cubic inches.
0.95 gives an allowance of 5% for loss of capacity.
© 1990 by Womack Machine Supply Co. This company assumes no liability for errors in data nor in safe and/or satisfactory operation of equipment designed from this information.