Final answer:
To estimate the required spindle power and the power needed at the motor, we calculate the force against gravity, adjust for the 75% of power used for this purpose, and account for the 15% energy transfer loss by dividing the spindle power by the motor's efficiency (0.85). For example, a 78 hp spindle power demand would require 91.76 hp at the motor, or 68473.36 watts.
Step-by-step explanation:
To estimate the power required at the spindle for a particular operation, and subsequently the power needed at the motor, considering a 15% energy transfer loss, we must calculate the net power output and then account for the loss. Knowing that 1 hp (horsepower) is equal to 746 W (watts), we can use the formula P = (force × distance) / time to find the power. This force is primarily against gravity, which for a motor vehicle on an incline is calculated using mg × sin(θ), where m is mass, g is the acceleration due to gravity, and θ is the angle of the incline (arctan(0.15) for a 15% grade). Once we have calculated the power required to move the car, we divide this by 0.75, considering that only 75% of the power is used to overcome gravity. We then increase the resultant power to account for the energy loss via the motor efficiency (in this case, an additional 15%).
Example Calculation:
Let's say the power required to move the car at constant velocity uphill is 78 hp. Accounting for the efficiency loss:
Power at the motor = Power at the spindle / Efficiency = 78 hp / 0.85 = 91.76 hp, which we then convert to watts: 91.76 hp × 746 W/hp = 68473.36 W.