It's a mathematical quirk arising from the relationship between torque
and power and it's only true for the same set of units which also
makes it entirely irrelevent to engine performance.
The commonly used formula is HP equals torque in ft-lb x rpm divided
by 5,252, in which case the lines will cross at 5,252 rpm.
However if the units of torque are changed to in-lb the formula
becomes HP equals torque x rpm divided by 63,025 and the lines will
cross at 63,025 rpm.
Since, by definition, power equals force by distance the quirk comes
about because of the conversion from force to torque, the latter being
the force acting at the radius of a circle... 1 foot in the first
formula, 1 inch in the second.
The mathematics is somewhat complicated as it involves reducing the
formula to its basic units and cancelling out the common factors.
There are fully worked examples online if you want to pursue it
Because it matters not where the lines cross as the power curve is
calculated directly from the torque curve based on actual dynamometer
readings (since power can't be measured directly).
The most relevant points on those curves are the peaks and rpm at
which they occur since they serve to indicate an engine's power band
(the rev range over which it performs most efficiently). This might
Also relevant might be the tendency of sales folk (and others) to
quote maximum torque in isolation of rpm as if it were a performance
indicator when it really means jack shit since flywheel torque isn't
what appears at the drive wheels (unless it's a Tesla). :)
Thank you for your help and advice.
I think the simplest answer was the one that explained torque is measured
and horsepower is simply calculated from that torque measurement using the
number 5,252 because of units.
If different units are used, the crossover point in RPM will be different.