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Compression Ratio worksheet

Grade 8 · CCSS 8.G.C.9

Solve each problem and show your work. Round answers to 2 decimal places where needed.

1.
Problem 1.
- Lengths in: Millimeters
- Bore: 76 mm
- Stroke: 86 mm
- Head gasket bore: 110 mm
- Compressed gasket thickness: 1.2 mm
- Piston deck clearance: 0.1 mm
- Combustion chamber volume: 76 cc
- Piston dish or dome volume: 2 cc
Find: Static compression ratio (to 1)
Answer
2.
Problem 2.
- Lengths in: Inches
- Bore: 3.75 in
- Stroke: 3.5 in
- Head gasket bore: 3.3 in
- Compressed gasket thickness: 0.028 in
- Piston deck clearance: 0.01 in
- Combustion chamber volume: 50 cc
- Piston dish or dome volume: 0 cc
Find: Static compression ratio (to 1)
Answer
3.
Problem 3.
- Lengths in: Inches
- Bore: 4.03 in
- Stroke: 3.5 in
- Head gasket bore: 3.8 in
- Compressed gasket thickness: 0.039 in
- Piston deck clearance: 0.01 in
- Combustion chamber volume: 50 cc
- Piston dish or dome volume: 8 cc
Find: Static compression ratio (to 1)
Answer
4.
Problem 4.
- Lengths in: Inches
- Bore: 4.06 in
- Stroke: 4 in
- Head gasket bore: 3.6 in
- Compressed gasket thickness: 0.039 in
- Piston deck clearance: 0 in
- Combustion chamber volume: 42 cc
- Piston dish or dome volume: 8 cc
Find: Static compression ratio (to 1)
Answer
5.
Problem 5.
- Lengths in: Millimeters
- Bore: 76 mm
- Stroke: 83 mm
- Head gasket bore: 90 mm
- Compressed gasket thickness: 1.5 mm
- Piston deck clearance: 0.2 mm
- Combustion chamber volume: 58 cc
- Piston dish or dome volume: 0 cc
Find: Static compression ratio (to 1)
Answer
6.
Problem 6.
- Lengths in: Millimeters
- Bore: 100 mm
- Stroke: 100 mm
- Head gasket bore: 120 mm
- Compressed gasket thickness: 0.5 mm
- Piston deck clearance: -0.1 mm
- Combustion chamber volume: 76 cc
- Piston dish or dome volume: 0 cc
Find: Static compression ratio (to 1)
Answer
7.
Problem 7.
- Lengths in: Millimeters
- Bore: 86 mm
- Stroke: 100 mm
- Head gasket bore: 90 mm
- Compressed gasket thickness: 0.5 mm
- Piston deck clearance: 0.5 mm
- Combustion chamber volume: 42 cc
- Piston dish or dome volume: 2 cc
Find: Static compression ratio (to 1)
Answer
8.
Problem 8.
- Lengths in: Inches
- Bore: 4.03 in
- Stroke: 3.48 in
- Head gasket bore: 4.4 in
- Compressed gasket thickness: 0.051 in
- Piston deck clearance: 0.025 in
- Combustion chamber volume: 50 cc
- Piston dish or dome volume: -5 cc
Find: Static compression ratio (to 1)
Answer
9.
Problem 9.
- Lengths in: Inches
- Bore: 4.125 in
- Stroke: 3.48 in
- Head gasket bore: 3.8 in
- Compressed gasket thickness: 0.015 in
- Piston deck clearance: -0.005 in
- Combustion chamber volume: 42 cc
- Piston dish or dome volume: 0 cc
Find: Static compression ratio (to 1)
Answer
10.
Problem 10.
- Lengths in: Millimeters
- Bore: 92 mm
- Stroke: 79 mm
- Head gasket bore: 80 mm
- Compressed gasket thickness: 0.7 mm
- Piston deck clearance: 0.5 mm
- Combustion chamber volume: 76 cc
- Piston dish or dome volume: 12 cc
Find: Static compression ratio (to 1)
Answer

Answer key: Compression Ratio worksheet

1. Static compression ratio (to 1): 5.34
1. Find the space one piston sweeps as it travels (swept volume): the bore's circle area times the stroke
  $\frac{π}{4} \times 76^{2} \times 86$ $= 390,135.542093 mm³$
2. Change to cubic centimeters (cc), the usual unit for engine size (1,000 mm³ = 1 cm³)
  $\frac{390,135.542093 mm³}{1,000}$ $= 390.135542 cc$
3. Find the space inside the head gasket: its opening's circle area times its compressed thickness
  $\frac{π}{4} \times 110^{2} \times 1.2$ $= 11,403.981333 mm³$
4. Find the deck volume, the gap above the piston up to the top of the block: the bore's circle area times the deck clearance
  $\frac{π}{4} \times 76^{2} \times 0.1$ $= 453.645979 mm³$
5. Add up all the space left when the piston is at the top (clearance volume): chamber + gasket + deck + dish, in cc. A dome counts as negative
  $76 + 11.403981 + 0.453646 + 2$ $= 89.857627 cc$
6. Divide the total space with the piston at the bottom by the space left at the top. That's how many times the mixture gets squeezed
  $\frac{390.135542 + 89.857627}{89.857627}$ $= 5.341708$
2. Static compression ratio (to 1): 12.37
1. Find the space one piston sweeps as it travels (swept volume): the bore's circle area times the stroke
  $\frac{π}{4} \times {3.75}^{2} \times 3.5$ $= 38.656316 in³$
2. Change to cubic centimeters (cc), the usual unit for engine size (1 in³ = 16.387064 cm³)
  $38.656316 in³ \times 16.387064$ $= 633.463522 cc$
3. Find the space inside the head gasket: its opening's circle area times its compressed thickness
  $\frac{π}{4} \times {3.3}^{2} \times 0.028$ $= 0.239484 in³$
4. Find the deck volume, the gap above the piston up to the top of the block: the bore's circle area times the deck clearance
  $\frac{π}{4} \times {3.75}^{2} \times 0.01$ $= 0.110447 in³$
5. Add up all the space left when the piston is at the top (clearance volume): chamber + gasket + deck + dish, in cc. A dome counts as negative
  $50 + 3.924433 + 1.809896 + 0$ $= 55.734329 cc$
6. Divide the total space with the piston at the bottom by the space left at the top. That's how many times the mixture gets squeezed
  $\frac{633.463522 + 55.734329}{55.734329}$ $= 12.365769$
3. Static compression ratio (to 1): 11.86
1. Find the space one piston sweeps as it travels (swept volume): the bore's circle area times the stroke
  $\frac{π}{4} \times {4.03}^{2} \times 3.5$ $= 44.644506 in³$
2. Change to cubic centimeters (cc), the usual unit for engine size (1 in³ = 16.387064 cm³)
  $44.644506 in³ \times 16.387064$ $= 731.592371 cc$
3. Find the space inside the head gasket: its opening's circle area times its compressed thickness
  $\frac{π}{4} \times {3.8}^{2} \times 0.039$ $= 0.442305 in³$
4. Find the deck volume, the gap above the piston up to the top of the block: the bore's circle area times the deck clearance
  $\frac{π}{4} \times {4.03}^{2} \times 0.01$ $= 0.127556 in³$
5. Add up all the space left when the piston is at the top (clearance volume): chamber + gasket + deck + dish, in cc. A dome counts as negative
  $50 + 7.248078 + 2.090264 + 8$ $= 67.338341 cc$
6. Divide the total space with the piston at the bottom by the space left at the top. That's how many times the mixture gets squeezed
  $\frac{731.592371 + 67.338341}{67.338341}$ $= 11.864425$
4. Static compression ratio (to 1): 16.02
1. Find the space one piston sweeps as it travels (swept volume): the bore's circle area times the stroke
  $\frac{π}{4} \times {4.06}^{2} \times 4$ $= 51.784757 in³$
2. Change to cubic centimeters (cc), the usual unit for engine size (1 in³ = 16.387064 cm³)
  $51.784757 in³ \times 16.387064$ $= 848.600122 cc$
3. Find the space inside the head gasket: its opening's circle area times its compressed thickness
  $\frac{π}{4} \times {3.6}^{2} \times 0.039$ $= 0.396972 in³$
4. Find the deck volume, the gap above the piston up to the top of the block: the bore's circle area times the deck clearance
  $\frac{π}{4} \times {4.06}^{2} \times 0$ $= 0 in³$
5. Add up all the space left when the piston is at the top (clearance volume): chamber + gasket + deck + dish, in cc. A dome counts as negative
  $42 + 6.5052 + 0 + 8$ $= 56.5052 cc$
6. Divide the total space with the piston at the bottom by the space left at the top. That's how many times the mixture gets squeezed
  $\frac{848.600122 + 56.5052}{56.5052}$ $= 16.018089$
5. Static compression ratio (to 1): 6.5
1. Find the space one piston sweeps as it travels (swept volume): the bore's circle area times the stroke
  $\frac{π}{4} \times 76^{2} \times 83$ $= 376,526.162718 mm³$
2. Change to cubic centimeters (cc), the usual unit for engine size (1,000 mm³ = 1 cm³)
  $\frac{376,526.162718 mm³}{1,000}$ $= 376.526163 cc$
3. Find the space inside the head gasket: its opening's circle area times its compressed thickness
  $\frac{π}{4} \times 90^{2} \times 1.5$ $= 9,542.587685 mm³$
4. Find the deck volume, the gap above the piston up to the top of the block: the bore's circle area times the deck clearance
  $\frac{π}{4} \times 76^{2} \times 0.2$ $= 907.291958 mm³$
5. Add up all the space left when the piston is at the top (clearance volume): chamber + gasket + deck + dish, in cc. A dome counts as negative
  $58 + 9.542588 + 0.907292 + 0$ $= 68.44988 cc$
6. Divide the total space with the piston at the bottom by the space left at the top. That's how many times the mixture gets squeezed
  $\frac{376.526163 + 68.44988}{68.44988}$ $= 6.500757$
6. Static compression ratio (to 1): 10.71
1. Find the space one piston sweeps as it travels (swept volume): the bore's circle area times the stroke
  $\frac{π}{4} \times 100^{2} \times 100$ $= 785,398.163397 mm³$
2. Change to cubic centimeters (cc), the usual unit for engine size (1,000 mm³ = 1 cm³)
  $\frac{785,398.163397 mm³}{1,000}$ $= 785.398163 cc$
3. Find the space inside the head gasket: its opening's circle area times its compressed thickness
  $\frac{π}{4} \times 120^{2} \times 0.5$ $= 5,654.866776 mm³$
4. Find the deck volume. The piston sticks up above the block here, so this space is taken away
  $\frac{π}{4} \times 100^{2} \times (−0.1)$ $= −785.398163 mm³$
5. Add up all the space left when the piston is at the top (clearance volume): chamber + gasket + deck + dish, in cc. A dome counts as negative
  $76 + 5.654867 + (−0.785398) + 0$ $= 80.869469 cc$
6. Divide the total space with the piston at the bottom by the space left at the top. That's how many times the mixture gets squeezed
  $\frac{785.398163 + 80.869469}{80.869469}$ $= 10.711924$
7. Static compression ratio (to 1): 12.6
1. Find the space one piston sweeps as it travels (swept volume): the bore's circle area times the stroke
  $\frac{π}{4} \times 86^{2} \times 100$ $= 580,880.481649 mm³$
2. Change to cubic centimeters (cc), the usual unit for engine size (1,000 mm³ = 1 cm³)
  $\frac{580,880.481649 mm³}{1,000}$ $= 580.880482 cc$
3. Find the space inside the head gasket: its opening's circle area times its compressed thickness
  $\frac{π}{4} \times 90^{2} \times 0.5$ $= 3,180.862562 mm³$
4. Find the deck volume, the gap above the piston up to the top of the block: the bore's circle area times the deck clearance
  $\frac{π}{4} \times 86^{2} \times 0.5$ $= 2,904.402408 mm³$
5. Add up all the space left when the piston is at the top (clearance volume): chamber + gasket + deck + dish, in cc. A dome counts as negative
  $42 + 3.180863 + 2.904402 + 2$ $= 50.085265 cc$
6. Divide the total space with the piston at the bottom by the space left at the top. That's how many times the mixture gets squeezed
  $\frac{580.880482 + 50.085265}{50.085265}$ $= 12.597832$
8. Static compression ratio (to 1): 12.56
1. Find the space one piston sweeps as it travels (swept volume): the bore's circle area times the stroke
  $\frac{π}{4} \times {4.03}^{2} \times 3.48$ $= 44.389394 in³$
2. Change to cubic centimeters (cc), the usual unit for engine size (1 in³ = 16.387064 cm³)
  $44.389394 in³ \times 16.387064$ $= 727.411843 cc$
3. Find the space inside the head gasket: its opening's circle area times its compressed thickness
  $\frac{π}{4} \times {4.4}^{2} \times 0.051$ $= 0.775471 in³$
4. Find the deck volume, the gap above the piston up to the top of the block: the bore's circle area times the deck clearance
  $\frac{π}{4} \times {4.03}^{2} \times 0.025$ $= 0.318889 in³$
5. Add up all the space left when the piston is at the top (clearance volume): chamber + gasket + deck + dish, in cc. A dome counts as negative
  $50 + 12.707688 + 5.22566 + (−5)$ $= 62.933348 cc$
6. Divide the total space with the piston at the bottom by the space left at the top. That's how many times the mixture gets squeezed
  $\frac{727.411843 + 62.933348}{62.933348}$ $= 12.558448$
9. Static compression ratio (to 1): 18.44
1. Find the space one piston sweeps as it travels (swept volume): the bore's circle area times the stroke
  $\frac{π}{4} \times {4.125}^{2} \times 3.48$ $= 46.506861 in³$
2. Change to cubic centimeters (cc), the usual unit for engine size (1 in³ = 16.387064 cm³)
  $46.506861 in³ \times 16.387064$ $= 762.110914 cc$
3. Find the space inside the head gasket: its opening's circle area times its compressed thickness
  $\frac{π}{4} \times {3.8}^{2} \times 0.015$ $= 0.170117 in³$
4. Find the deck volume. The piston sticks up above the block here, so this space is taken away
  $\frac{π}{4} \times {4.125}^{2} \times (−0.005)$ $= −0.06682 in³$
5. Add up all the space left when the piston is at the top (clearance volume): chamber + gasket + deck + dish, in cc. A dome counts as negative
  $42 + 2.787722 + (−1.094987) + 0$ $= 43.692735 cc$
6. Divide the total space with the piston at the bottom by the space left at the top. That's how many times the mixture gets squeezed
  $\frac{762.110914 + 43.692735}{43.692735}$ $= 18.442509$
10. Static compression ratio (to 1): 6.54
1. Find the space one piston sweeps as it travels (swept volume): the bore's circle area times the stroke
  $\frac{π}{4} \times 92^{2} \times 79$ $= 525,161.194345 mm³$
2. Change to cubic centimeters (cc), the usual unit for engine size (1,000 mm³ = 1 cm³)
  $\frac{525,161.194345 mm³}{1,000}$ $= 525.161194 cc$
3. Find the space inside the head gasket: its opening's circle area times its compressed thickness
  $\frac{π}{4} \times 80^{2} \times 0.7$ $= 3,518.583772 mm³$
4. Find the deck volume, the gap above the piston up to the top of the block: the bore's circle area times the deck clearance
  $\frac{π}{4} \times 92^{2} \times 0.5$ $= 3,323.805027 mm³$
5. Add up all the space left when the piston is at the top (clearance volume): chamber + gasket + deck + dish, in cc. A dome counts as negative
  $76 + 3.518584 + 3.323805 + 12$ $= 94.842389 cc$
6. Divide the total space with the piston at the bottom by the space left at the top. That's how many times the mixture gets squeezed
  $\frac{525.161194 + 94.842389}{94.842389}$ $= 6.537199$