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 find the stroke length of the engine, we can use the formula for horsepower (\(HP\)) in terms of the dimensions and performance of the engine: \[ HP = \frac{(IMEP \times A \times L \times N)}{33,000} \] where: - \(HP\) is the horsepower (1900 HP) - \(IMEP\) is the indicated mean effective pressure (1510 psi) - \(A\) is the area of the piston (in square inches) - \(L\) is the stroke length (in inches) - \(N\) is the engine speed (number of power strokes per minute) Since this is a 6-cylinder engine, each cylinder works in a two-stroke cycle for every crankshaft rotation, meaning effective power strokes per minute for a four-stroke engine is half the RPM. Let's find the area \(A\) first: \[ A = \pi \left(\frac{B}{2}\right)^2 \] where \(B\) is the bore in inches. Given: - Bore \(B\) = 3.8 inches Thus, \[ A = \pi \left(\frac{3.8}{2}\right)^2 \approx 11.34 \text{ in}^2 \] ### Effective Power Strokes For a 6-cylinder engine at 1270 RPM: 1. Each cylinder produces a power stroke once every two revolutions (for a four-stroke engine). 2. Thus total effective strokes (assuming a four-stroke engine) = \[ N = 1270 \times \frac{6}{2} = 3810 \text{ strokes/min} \] ### Rearranging the Horsepower Formula We need to express stroke length \(L\): \[ L = \frac{HP \times 33,000}{IMEP \times A \times N} \] Plugging in the numbers: - \(HP = 1900\) - \(IMEP = 1510\) - \(A \approx 11.34\) - \(N = 3810\) Giving, \[ L = \frac{1900 \times 33,000}{1510 \times 11.34 \times 3810} \] Calculating: \[ L = \frac{62700000}{1510 \times 11.34 \times 3810} \approx 3.77 \text{ inches} \] To convert to feet: \[ L \approx \frac{3.77}{12} \approx 0.31 \text{ feet} \] So, the stroke length of the engine is approximately **0.31 feet** when rounded to two decimal places.