Calculate the stroke length (in feet) of an engine with the following parameters: 6 cylinders, has an indicated mean effective pressure (IMEP) of 1510 psi per cylinder, a bore of 3.8 inches, operating at 1270 rpm , and operates at 1900 horsepower. Round to 2 decimal places.

To calculate the stroke length of the engine, we can use the following formula that relates the engine's power output, IMEP, engine speed, and displacement: \[ \text{Power} = \frac{IMEP \times \text{Displacement} \times \text{RPM}}{33,000} \] Where: - Power is in horsepower (hp) - IMEP is in psi - Displacement is in cubic inches (ci) - RPM is the engine speed in revolutions per minute - 33,000 is a conversion factor to convert from foot-pounds per minute to horsepower ### Step 1: Calculate the Displacement The displacement of a single cylinder can be calculated using the formula: \[ \text{Displacement per cylinder} = \frac{\pi}{4} \times \text{Bore}^2 \times \text{Stroke} \] The total displacement for all cylinders is: \[ \text{Total Displacement} = \text{Displacement per cylinder} \times \text{Number of cylinders} \] ### Step 2: Rearranging the Power Formula We can rearrange the power formula to solve for the total displacement: \[ \text{Total Displacement} = \frac{\text{Power} \times 33,000}{IMEP \times \text{RPM}} \] ### Step 3: Plugging in the Values Given: - Power = 1900 hp - IMEP = 1510 psi - RPM = 1270 - Number of cylinders = 6 - Bore = 3.8 inches Calculating the total displacement: \[ \text{Total Displacement} = \frac{1900 \times 33,000}{1510 \times 1270} \] Calculating the numerator: \[ 1900 \times 33,000 = 62,700,000 \] Calculating the denominator: \[ 1510 \times 1270 = 1,915,700 \] Now, calculating the total displacement: \[ \text{Total Displacement} = \frac{62,700,000}{1,915,700} \approx 32.69 \text{ cubic inches} \] ### Step 4: Calculate Displacement per Cylinder Now, we divide the total displacement by the number of cylinders: \[ \text{Displacement per cylinder} = \frac{32.69}{6} \approx 5.45 \text{ cubic inches} \] ### Step 5: Calculate Stroke Length Now we can use the displacement per cylinder to find the stroke length. Rearranging the displacement formula gives us: \[ \text{Stroke} = \frac{4 \times \text{Displacement per cylinder}}{\pi \times \text{Bore}^2} \] Substituting the values: \[ \text{Stroke} = \frac{4 \times 5.45}{\pi \times (3.8)^2} \] Calculating the denominator: \[ \pi \times (3.8)^2 \approx 3.14159 \times 14.44 \approx 45.39 \] Now calculating the stroke: \[ \text{Stroke} = \frac{21.8}{45.39} \approx 0.48 \text{ inches} \] ### Step 6: Convert Stroke Length to Feet To convert inches to feet, we divide by 12: \[ \text{Stroke in feet} = \frac{0.48}{12} \approx 0.04 \text{ feet} \] ### Final Result The stroke length of the engine is approximately: \[ \text{Stroke Length} \approx 0.04 \text{ feet} \] Thus, the final answer rounded to two decimal places is: \[ \text{Stroke Length} \approx 0.04 \text{ feet} \]