Problem: Number of Cycles

“I plan to put an eight (8)-ft. elevator in my house using an air-over-oil system in case of power outages. My air compressor has a 75-gallon tank and kicks on at 80 psi. If I were to use a four (4)-in. cylinder for a total load of 350 lbs., theoretically how many cycles would I have with a loss of power, starting at 80 psi?”

Use 50 cubic inches of air space on top of the oil tank and back to the regulator. Assume 100% efficiency.

Find Out The Solution

Solution: 9 Cycles

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Load on elevator 350 lbs.

Load on cylinder 700 lbs. (2:1 Mechanical disadvantage)

Cylinder diameter is 4” Area = 12.566 in².

Cylinder volume = 12.566 x 48” (2:1 Mech. Disadvantage) = 603 in³ + 50 in³ in the airline = 653 in³ / cycle

Required PSI = 700 lbs. / 12.566 in² = 55.7 PSI

Tank Volume = 75 gallons x 231 in³ / gallon = 17,325 in³

Because of the changing in pressure as we use air volume from the tank, we need to convert our cubic inches into standard cubic inch.  This can be done by finding the compression ratio and multiplying it by the cubic inches.  Another way of looking at this is the number of cubic inches that the air compressor would need to take in to complete the job.  A formula that works for that is gage pressure / 14.7 + 1 =.80 / 14.7 + 1 = 6.442 (C. R.)   (This means that it takes 6.442 cubic inches of free air to get 1 in³ of compressed air at 80 PSIG.  That is what the air compressor draws in for each cubic inch it delivers at 80 PSIG.)

6.442 (C.R.)  x 17,325 in³ = 111,610.7 standard cubic inches in the tank

Minimum air pressure needed is 55.7 PSIG

55.7 / 14.7 + 1 = 4.789 C.R.   47.789 x 17,325 = 82,971 standard cubic inch that will remain in the tank at minimum PSI

Subtracting the minimum from the maximum = 111,610.7 – 82,971 = 28,639 useable standard cubic inches.

Again, convert cubic inches required to standard cubic inches required:

55.7 / 14.7 + 1 = 4.789 x 653 in³ (needed per cycle) = 3127 standard cubic inches per cycle

Take useable volume in tank and divide by required cubic inch per cycle:

28,641.3 / 3127 = 9 cycles theoretically

Note:  If one were to figure air usage at 67% efficient, you could count on at least six (6) complete cycles because the cylinder is used as a single-acting cylinder.

Deadline past. Not available for submissions.

By Ernie Parker, AI, AJPP, AJPPCC, S, MT, MM, MIH, MIP, MMH,
Fluid Power Instructor, Hennepin Technical College, EParker@Hennepintech.edu

This teaser is printed in the Fluid Power Journal. Those who submit the correct answer before the deadline will have their names printed in the Society Page newsletter and in Fluid Power Journal. The winners will also be entered into a drawing for a special gift.

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