To estimate the speed of a vehicle with 138 horsepower, several factors need to be considered, including the vehicle's weight, aerodynamic design, and drivetrain efficiency.
Assuming an average passenger car with a curb weight of around 3,000 pounds (1,361 kilograms) and a frontal area of 22 square feet (2.04 square meters), and a 5-speed manual transmission with a final drive ratio of 3.5:1, and rolling resistance and aerodynamic drag coefficients:
- Rolling resistance coefficient (Crr): 0.01
- Aerodynamic drag coefficient (Cd): 0.3
Using the following equation:
Speed (mph) = √( (Horsepower x 375) / (Vehicle Weight x (Crr + (Cd x Air Density x Frontal Area x Speed^2/2)) ) )
Where:
- Horsepower: 138 hp
- Vehicle weight: 3000 lbs
- Crr: Rolling resistance coefficient
- Cd: Aerodynamic drag coefficient
- Air density: 0.002377 slugs/cubic feet (at sea level)
- Frontal area: 22 square feet
- Speed: the speed we're trying to determine
Solving the equation for speed:
Speed (mph) ≈ √((138 x 375) / (3000 x (0.01 + (0.3 x 0.002377 x 22 x Speed^2/2)))) ≈ 115.6 mph
Therefore, a vehicle with 138 horsepower, under these assumed conditions, can theoretically reach a top speed of approximately 116 miles per hour (188 kilometers per hour).
It's important to note that this calculation is an approximation, and actual speeds may vary depending on specific vehicle configurations and environmental conditions.
