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Is there a relation between engine size and its power to weight ratio? For example if you shrink the engine to half the size will it have exactly half the power?

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No, more like 1/8. Power (and weight) is most closely related to volume, which changes with the cube of the linear dimensions.

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  • $\begingroup$ so how will the power change after reducing volume by half? $\endgroup$
    – X10D
    Apr 4 '20 at 6:37
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as you shrink a heat engine, its volume (in which power is developed) falls faster than its surface area (through which losses occur) which means a small engine will inherently be lossier than a large engine of the same design. This scaling relationship is universal, which means that engine designers prefer one large engine instead of two smaller ones.

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