In article ,
(Peter Stickney) writes:

Just back - I'll get to it tomorrow - right now I'm wading through the
"British Night Bombers vs. the P-38" thread.

Here I am - and here it goes:
Basically, aircraft engines have two different types of power delivery
- Constant Power, like a reciprocating engine, or a turboprop's output
shaft, and
- Constant Force, like a jet engine, or the exhaust thrust portion of
a turboprop.
Turning Power into Thrust is something that starts out simple,
but, as Real Life intrudes, gets a bit complicated.
I'll stick to SAE/British Engineering units for now, too.

To start with, there's a very simple formula that relates Force to
Power: 1 HP = 550 lb(force) ft/sec, or basically the amount of oomph
needed to lift 550 lbs 1 ft in 1 second. When you look at it, you
see that we've got a Force (lbs) and a speed (ft/sec). So, the way to
determine how much horsepower you're getting from a particular force
(thrust) is HP = (Thrust(lbs) * Speed(fps))/ 550 ft/sec .
Since 550 ft/sec is 375 mph, let's rewrite it as:
HP = (Thrust (lbs)* Speed (mph))/375 mph.

Or, rearranging things a bit, Thrust = HP * 375/Speed (mph).

So, for a constant Horsepower, the Thrust is very high at low speeds,
and it tapers off as speed increases.
For a Constant Force type of engine, teh Thrust Horsepower generated
increases as the speed increases.
For example, let's round your C-130 example (Assuming it's all Shaft
Horsepower - more on that later) to 5,000 HP, and let's see what
we get for Thrust.
We'll also take your J85 from the F-5, at 5,000# thrust, and see what
we get for Horsepower.

Constant Power Constant Thrust
HP Speed Thrust HP Speed Thrust
MPH Lbs MPH Lbs
5000 100 18750 1333 100 5000
5000 200 9375 2666 200 5000
5000 300 6250 4000 300 5000
5000 400 4697 5333 400 5000
5000 500 3750 6667 500 5000
5000 600 3125 8000 600 5000

So, as you can see, with constant power, teh thrust starts out very
high, and drops off rather markedly as speed increases. This is great
for hauling a Heavy Herc off of a hot runway, but if you want to go
much faster than 500 mph, you're going to need an awful lot of
horsepower. (That's why late war & post- WW2 fighters topped out in
the high 400 mph range, and why the propeller driven speed records
haven't changed mich in about 70 years.
The jet starts out with a _lot_ lower power, but since the thrust
remains constant, it really picks up as speed increases.
This is why it's possible for a high-powered piston-engined fighter to
outperform a jet (especially an early jet, like the Me 262, which was
really rather underpowered) in the lower speed ranges. A jet at low
speeds doesn't have a lot of excess power for accelerating, climbing,
or turning, and the prop has tons of it.

That was the simple part.
WHen it gets complicated, we start throwing in stuff about Propeller
Efficiencies and adjustable pitch propellers vs fixed pitch, & so on.
Propellers are complicated beasts, and they tend to fudge things up at
either very high or very low speeds. We can get into it later, if you
want.

--
Pete Stickney
A strong conviction that something must be done is the parent of many
bad measures. -- Daniel Webster