Gator's Challenge

Energy is conserved. That's the first law of thermodynamics, and in the
time of James Watt, it was promulgated by the great American scientist,
Ben Thompson, or as he was known after we booted him out of the
country for his radical politics, "Count Rumford"
.... but that's a side issue, let's keep it simple.

Ben studied machining, he knew it took lots of work to bore cannon, and
the workpiece got hot (though today, we know where to buy a cure for that,
$28 a gallon). He made the connection. The work done BOTH made
chips AND heat, but duller tools made less chips and more heat
... but that's a side issue, let's keep it simple.

The 'work' aka 'energy' consumed (the input) was a conserved quantity,
you could total up the heat and chips (the output), and know how much

(1) horse feed
(2) coals from Newcastle
(3) billable electricity
(4) water volume through the flume of a given waterwheel

went in. Any of those inputs become work, produce the output.

The formula for energy in the machine tool that bored those cannon was:

Energy = Torque * Angular_speed * Time

because nothing would make chips without torque, without movement, without time.
And you can convert (because energy is conserved) from an ideal rope wrapped
around a drum, to

Energy =Rope_tension * Velocity * Time

because that rope and the drum radius make a torque, and the drum diameter
and Angular_speed = Velocity / ( 2pi * Drum_radius) :== radians per second
which follows from

Torque = Rope_tension * Drum_radius and
Velocity = 2pi * Drum_radius * Angular_speed

So, depending on the power-transmission chain, there's lots of similar
formulas, all toting up the energy, or (leaving out time which is common
to all these formulas) relating forces (and generalized force-like quantities)
and displacements (and generalized displacements) with power
(which is truly general, and needs no generalization).

Energy/ Time = Power = Rope_tension * Velocity
can also be expressed as
Watts = Newtons * Meters_per_second

and with a suitable conversion from SI units to the world of working horses,

Horsepower / (745 HP/Watt) = Newtons * Meters_per_second

Other (generalized forces) equations for power are all in the form of
a product of an intensive property (that isn't different for an ant or an
elephant, doesn't scale with power needs), and an extensive property
(which DOES scale). For economics, it's the extensive thing that costs
you more when you use more power...

Power = Voltage * Current
Power = Friction * Velocity
Power = Dam_height * Water_mass_flow
Power = Torque * Angular_speed
Power = Fuel_specific_energy_content * Fuel_delivery_rate
Power = Horse_daily_feed * Horsies_hired
Power = P40_decay_energy * (Potassium_40_atoms/P40_decay_lifetime)

but unless you are in the habit of powering Earth's volcanoes, that last one is
kinda... esoteric.

Really, I TRIED to keep it simple! That just isn't my forte.
 
The apples and carrots might work but changing octane in your gas will not help horsepower. A higher octane gas will allow you to make changes to your engine that result in more horsepower (increase compression ratio, advance timing, etc.) but octane in and of itself will not make any difference in an engines performance.


Not true today. In todays muscle cars EPA says they have to run on regular 87oct. Put them on a dyno and they fall short of rated HP and TRQ. Put 97oct in and It will hit rated numbers. This is because they are detuned to run on 87. In my mustang I picked up 5-6 hp and 15ftlb trq. Once I retuned it I picked up 20hp and 30 ftlb.
 
There is no energy (BTU) in octane. Zero, zip, nada. Therefor octane cannot improve performance. A gallon of gas has about 12,000 BTUs regardless of octane rating - even 110 AvGas. Something else had to have changed (and most dynos are very unreliable).
Octane is a measure of a fuel's tendency to ignite under pressure. Lower octane gasolines ignite at lower pressures, which is why higher octane gas helps reduce knocking from compression.
There may be other diferences in the 2 blends of gasoline that affected the power from the fuel, but it wasn't octane.
 
As stated, a higher "Octane" level raises the auto ignition temperature of gasoline, not the energy contained within.
Since an engine cylinder is a fixed volume based on bore and stroke, some modern high performance engines can sense knock and adjust (retard) the timing to prevent knock (pre-ignition), though, in so doing, decreases performance.
With higher octane fuels, the engine controls can advance the timing slightly. This does two things:
1. It effectively increases the compression since the fuel/air mixture is already combusting/expanding before pistol hits top dead center.
2. It burns the fuel more completely releasing more energy.
The net result being a measurable increase in both torque and horsepower.

Much of this has to do with the "Speed" of combustion. When a spark plug fires, the fuel/air mixture burns at a given rate based on the temperature of the mixture also known as "Flame Front Speed".
Another factor is the "Volume" of the combustion chamber. If you could see the crank shaft and pistons in an engine, what you'd see is that as the crank shaft rotates the velocity of the piston would increase as it went from top dead center until it reaches 90 degrees of rotation of the crank. From 90 degrees to 180 degrees (bottom dead center), it downward velocity of the piston reduces. This process repeats as it travels back up from 180 degrees to 360 degrees of crank shaft rotation.
When the RPM of an engine increases, the change in volume per unit time increases since the piston is moving up and down at a faster rate. This has the effect of reducing the "Compression Ratio" of the engine during its cycle. Engine designers account for this (to the extent possible) by "Advancing the Ignition" of the spark plugs. This causes the fuel/air mixture to start combusting before the piston hits Top Dead Center. During the combustion process, the gases are heated and expand. If the piston is still moving upward (compression stroke), this increases the pressure in that volume increasing the pressure and temperature in the cylinder which causes the combustion process to happen at a faster rate which, in turn, increases cylinder pressure which applies a greater force to push the piston down.
With lower octane fuel, pockets of the fuel/air mixture can ignite at a lower temperature. If the piston is still on the upstroke when this happens, it raises the pressure in the area above the piston which reduces the velocity of the pistons upward travel, acting like a brake. This is what causes "Engine Knock". It's the sound resulting from the gases impacting the piston as it is still traveling upward during the compression stroke.
If the timing is advanced too far, the condition gets worse and can lead to engine damage. Retard the ignition to far (sparks later in the cycle) and the cylinder volume is increasing faster than the flame front reducing the combustion rate which robs the engine of power.
 
One time I had some left over 110 octane leaded race gas, so I used it in the riding lawn mower. It went up the hill better and seemed to get better mileage (Mowage). I think the blend was energy denser than regular unleaded gas, more BTUs. On a side note, The song Proud Mary, by CCR has a verse: Cleaned a lot of plates in Memphis, Pumped a lot of tane down in New Orleans. Do you think the word "tane" is a reference to gasoline?
 
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