Which statement correctly describes gear ratio, torque multiplication, and efficiency in a transmission?

Which statement correctly describes gear ratio, torque multiplication, and efficiency in a transmission?

• A. Gear ratio is output speed divided by input speed; torque multiplies by the ratio minus losses; efficiency reduces the ideal values due to losses; higher ratio yields higher torque but lower speed; losses reduce actual values.
• B. Gear ratio is input speed divided by output speed; torque multiplies by velocity; efficiency decreases power.
• C. Gear ratio is a measure of energy conversion; torque is independent; efficiency is always 100%.
• D. Gear ratio is output torque divided by input torque; speed equals gear ratio; efficiency increases with load.

Answer: (A)

In a transmission, the gear ratio expresses how the output speed compares to the input speed and, importantly, how torque is traded for speed. The central idea is that gear trains convert some input speed into output torque, at the cost of reduced output speed, while overall power is reduced by losses. Think of the ideal case where power is preserved apart from losses: the output torque is essentially scaled by how much the speed is reduced. If the gear arrangement causes the output to run slower than the input, the torque at the output increases by roughly that same ratio, but real systems have losses—friction, heat, and other inefficiencies—that lessen the actual torque. This is captured by saying the output torque is the product of the input torque, the gear ratio, and the efficiency (a number less than 1). So you multiply by the ratio to get the theoretical gain, then apply the efficiency to account for losses. Efficiency is a measure of how much of the input power actually appears at the output. Because efficiency is less than one, some power is always lost as heat or other forms of loss, which is why the actual output torque and speed differ from the ideal, lossless case. The practical takeaway is that increasing the gear ratio (more reduction) increases torque at the output but lowers the output speed, and losses reduce the actual values from their ideal, lossless predictions. The other statements either misstate how speeds, torques, and efficiency relate or claim unrealistic absolute values for efficiency.

In a transmission, the gear ratio expresses how the output speed compares to the input speed and, importantly, how torque is traded for speed. The central idea is that gear trains convert some input speed into output torque, at the cost of reduced output speed, while overall power is reduced by losses.

Think of the ideal case where power is preserved apart from losses: the output torque is essentially scaled by how much the speed is reduced. If the gear arrangement causes the output to run slower than the input, the torque at the output increases by roughly that same ratio, but real systems have losses—friction, heat, and other inefficiencies—that lessen the actual torque. This is captured by saying the output torque is the product of the input torque, the gear ratio, and the efficiency (a number less than 1). So you multiply by the ratio to get the theoretical gain, then apply the efficiency to account for losses.

Efficiency is a measure of how much of the input power actually appears at the output. Because efficiency is less than one, some power is always lost as heat or other forms of loss, which is why the actual output torque and speed differ from the ideal, lossless case.

The practical takeaway is that increasing the gear ratio (more reduction) increases torque at the output but lowers the output speed, and losses reduce the actual values from their ideal, lossless predictions. The other statements either misstate how speeds, torques, and efficiency relate or claim unrealistic absolute values for efficiency.