Question re: inversely proportional pressure vs velocity

[TWB]

Howzzat for a title? I had trouble stating the actual question clearly too. I hope it makes sense.
I have a question that has been bugging me for years, and this seems the place with people with enough experience and skill to clue me in. How is it that a powder load that produces less pressure, can produce a higher velocity than another powder that gives a much higher pressure, but with a lower velocity?
Specific case: .357 mag. Hodgdon loading manual; Li'l Gun at 25,800cup -->1577fps, and HS-6 at 41,900cup --> 1375fps. Both these are obtained with a Hornady 158gr. XTP bullet. How does a charge producing 16,000 cup less pressure, produce a velocity >200fps faster, with the same weight bullet, in the same bbl. length test apparatus?
(I know "copper units" is a sucky and inaccurate way to determine pressure, but the principal question is not altered by SAAMI's bad judgment. The values are relative to each other.)
Even using the idiotic barrel length mandated by SAAMI for testing .357 mag loads (10 inches……a Freudian barrel length we can relate to from other ventures), the maximum push exerted by a given load, should produce a proportional velocity of the bullet. Why are not proportional velocities produced relative to pressures? I doubt that friction would apply in this length bbl. It is unlikely that the powders have completely burned at this point.
There are numerous examples of this phenomenon scattered around many reloading manuals. This result is counterintuitive. If you use more strength to throw a baseball, you can reasonably expect the ball to fly faster to the target, and strike with more energy than the same ball lobbed at leisure.
A search produced a magnificent explanation of velocity as relates to powder efficiency by Unclenick, but I still haven't found an answer relating to relative peak pressures vs velocity.
My age weakened brain has fixated on this. Please help me.

twb

[Wildalaska]

IF I recall correctly, IFIFIFIFIF, it has to do with pressure curves and peak pressures...ie a slower burner has lower pressure spread out over more time, while a fast burner spikes from lower pressures in a shorter time...

measure pressures are usually measured as peak

WilddidimakesenseAlaska

[crowbeaner]

I think it has to do with the time/pressure curve more than the actual burning rate of the powder. I have the same results in my .222 with RL7 and IMR 4320. RL7 is faster and gives 100 fps more velocity than the 4320. Did I make sense? Maybe it has to do with barrel time.

[Wildalaska]

yes but wont a faster powder reach peak pressure faster.?....ah but its not just burn rate but the energy delivered by the powder...isn't it then a function of the burn rate, the time of burn and the "explosive" power of the powder...

Am I making sense?

HELLLLLLLLLLLLLLLLLLLLLLLLP

WildcomeonimsoinarticulateAlaska

[LHB1]

It is a function of both pressure and how long that pressure is applied to the bullet. While a fast burning powder may produce a higher max pressure, this max pressure drops off very quickly. A slower burning powder that produces a slightly lower pressure longer can maintain acceleration of the bullet longer and thus yield a higher velocity.

Good shooting and be safe.
LB

[Chris McDermott]

The overall pressure curve is the correct answer. Fast burning powders burn quickly, often finishing their burn before the bullet leaves the case. So the pressure rises very fast as the volume of the case is fairly small; but the pressure also falls quickly as the bullet moves down the barrel quickly increasing the volume holding the hot gases. Slower powders don't finish burning until the bullet is an inch or more down the barrel, so the hot gases have a much larger volume to occupy, allowing much more powder to be loaded before reaching the same pressure level as the fast powder. Since you have a much larger amount of hot gases in a much larger volume, the pressure falls much more gradually as the bullet goes down the barrel. This gives much more "push" to the bullet, forcing it to go faster even though the peak pressure may have been less.
Another way to consider this is to look at how much powder is actually being loaded, slower powders have much more powder loaded into the cartridges, which represents much more potential energy being present in the case. Yes, single base powders have less energy per grain than double base powders that contain nitroglycerine as well as nitrocellulose; but the difference is on the order of 25% more energy, while slow burning rate powders will get 2-3 times as much powder loaded into a cartridge than fast powders.

[Wildalaska]

So I was right in my own garbled way!

WildinsertjumpingwithjoysmileyhereAlaska

[TWB]

Gentlemen, I thank you for helping me with this. Wildalaska, thanks also for struggling to make things sound sensible. For some reason, I had the same problem just trying to explain what I was getting at....took more than an hour, then saved it and took another shot the next day.
Anyhow, thanks again to all of you for the help.
twb

[redhawk41]

Calculus anybody?

It has been awhile so anyone with more current experience please correct me where I am mistaken.

The velocity of the bullet is related to the work done on the bullet (energy transfer), or the integral of the pressure-time function. The integral solution represents the area under the curve.

In more layman's terms a curve with a tall narrow spike, which represents a fast burning powder and a higher peak pressure, will have less area than a short fat curve which represents a slower burning powder and lower peak pressure.

From an engineering standpoint a compromise between pressure magnitude and duration can be reached which maximizes velocity while mitigating some other variable such as powder charge weight, charge density, peak pressure, etc.

This is why software like Quickload exists and is well worth the purchase price.

[Archie]

But I'm going to re-state it anyway.

The pressure shown in the loading manuals is the peak pressure. It is an instantaneous measurement. This is what will blow up the gun if it goes too high.

What pushes the bullet is the 'average pressure' (that's my term, don't look for it anywhere else) and is the average pressure from the time the primer ignites the powder until the bullet leaves the barrel. The average pressure is what drives the bullet. As Mr. McDermott said, this is the 'area under the curve' of the representation of the powder burn/pressure curve on a graph.

So saying, one could have a 'peak pressure' that ruptures the chamber without getting the bullet out of the barrel. On the other hand, one can have a high velocity without straining the mechanism at all.