Calculate what size cylinder is needed to hold the load.
Metric Solution
1. Calculate the cylinder force on all three jib booms using a moment equation.
Note: There are no units of measure (mm or in) given for the perpendicular distances to the pivot points. This is because it is the ratio that is needed. The units do not matter.
Boom “A” has a 2201.96 N load.
2201.96 N x 83.1 / 27.6 = 6,642 N
Boom “B” has a 2201.96 N load.
2201.96 N x 96 / 23.2 = 9128 N
Boom “C” has a 2201.96 N load.
2201.96 N x 83.1 / 16.9 = 10,847 N
(Heaviest Load)
2. Load on cylinder / MPa = 10,847 N / .69
= 15,699.69 mm²
3. Calculate area of rod:
A = D² x .7854; 31.75² x .7854 = 791.73 mm²
4. Because the piston area required is the area of two pistons minus the area of the rod, you should use this equation. Total piston areas = 2A – 791.73 mm².
5. Total area 15,699.69 mm² = 2A – 791.73 mm².
16,491.43 mm² = 2A
A = 8,245.71 mm²
6. Diameter = sqrt (A / 0.7854).
sqrt (8,245.71 / 0.7854) = 102.46
US Customary
1. Calculate the cylinder force on all three jib booms using a moment equation.
cc is the perpendicular distance to the pivot points. The force is 495 pounds.
Boom “A” has a 495 pound load.
495 x 83.1 / 27.6 = 1,490.38 pounds
Boom “B” has a 495 pound load.
495 x 96 / 23.2 = 2,048.28 pounds
Boom “C” has a 495 pound load.
495 x 83.1 / 16.9 = 2,433.99 pounds
(Heaviest Load)
2. Load on cylinder / psi = Area 2,433.99 / 100 = 24.34 in²
3. Calculate area or the rod.
A = D²x .7854; 1.25² x .7854 = 1.23 in²
4. Because the piston area required is the area of two pistons minus the area of the rod, you should use this equation. Total piston areas = 2A – 1.23 in².
5. Total area 24.34 in² = 2A – 1.23 in².
25.57 in² = 2A
A = 12.78 in²
6. Diameter =sqrt (A / 0.7854).
sqrt (12.78 / 0.7854) = 4.03
Checking our math 102.46 mm / 25.4 = 4.03 in
