[nj709]

Thanks for splainin' it to me. I've always wanted a car that is smaller on the outside than it is on the inside. Got any rithmetic for that?

 

[ugh762x39]

Ask the owl holding the Tootsie-Pop.

 

[bmcgilvray]

Just how long does it take a car to get to a quarter of a mile?

 

[gasmitty]

The original question, posted here, was: "How long does a bullet spend accelerating in the barrel of a rifle?"

I think it's safe to say the vast majority of people on this forum know that varies significantly, depending upon bullet caliber, bullet mass, cartridge propellant, cartridge primer and primer type, not to mention the length of the barrel, twist of rifling grooves, depth of the rifling grooves, width of the rifling grooves, type of barrel steel, the way the barrel was made (cast, forged, hammered, drilled, rolled, cut/lathed), and the way the barrel was heat-treated (hardening).

Having take a class or three in materials engineering, I do believe this can be reduced to some approximating equations, but some of the coefficients must be placarded. That is, they're discrete elements, which vary in steps between the above mentioned factors, such as the type of powder that was used. I'm not going to begin to dig into my college texts to derive a single equation t=f(x), but let's at least figure out which components can be parameterized and which will require tabular data. Here's my initial stab at it:

Continuous (can be included in the equation using algebraic and/or calculus equations):

bullet caliber
bullet jacket (affects friction)
bullet composition (jacket and composition affect in-barrel deformation, which affects both friction and its ability to seal against propellant gases)
bullet mass
cartridge propellant
length of the barrel
twist of rifling grooves
depth of the rifling grooves
width of the rifling grooves

Discrete (varies widely from one brand to another, and so much be introduced via placard coefficients into the equation):

cartridge propellant
cartridge primer (via make and model)
barrel make and model*

*barrels: So many factors go into making a barrel that it's extremely difficult to parameterize them all. It's easier to test a specific set of barrels all made not to the same manufacturer's specification, but rather, all made in precisely the same way, and note the performance under different rounds, than it is to attempt to parameterize sub-elements of the barrel like:

• type of barrel steel (although, if specific ratios off the steel phase diagram are known, they might be able to be parameterized, above)
• the way the barrel was made (cast, forged, hammered, drilled, rolled, cut/lathed)
• the way the barrel was heat-treated (hardening)

Why? Because it's there. It may also help hand-loaders get the most out of their loads and propellants while remaining on this side of the limits of safety.

On a more practical note, it's sufficient for nearly all practical purposes to use the cartridge manufacturer's specifications with respect to both round performance, and if you're loading your own, use the powder's performance charts to determine how much to use given the caliber and mass of bullet.

Then, there's this outstanding resource.

And this one.

Finally, there's always Grandpa's answer: 'Bout that long...

If you want a quick approximation:
The bullet (or cannonball...) accelerates from zero to its muzzle velocity 'MV' in 't' seconds. So its average velocity 'Vavg' while in the barrel is (MV + 0)/2. Divide the barrel length by Vavg (keep units straight) and you'll have the time 't' of the bullet's duration in the barrel.
Example: muzzle velocity is 2000 ft/sec, so Vavg is 1000 feet/sec. Barrel length is 1 foot. 1 ft/(1000 ft/sec) = 0.001 sec.
This is just a first-order approximation that assumes linear acceleration, which is unlikely due to propellant burn rates. But it'll be better than one order of magnitude, and probably good within a factor of 2.

 

[bmcgilvray]

Ok, Gary. I even like to ponder internal ballistics, but I just made an F in your class today. Hah!

 

[gasmitty]

Bryan, your 220 Swift example is one I've used for years when discussing the ballistics of the M1 Abrams gun. My comparison is that the fastest rifle round a shooter can buy over the counter shoots a 40 grain bullet at a little over 4000 ft/sec. The 120 mm smoothbore gun on the Abrams launches a 6-pound projectile at around 7000 ft/sec!

 

[MJK]

For a projectile exiting a 24” barrel at 2600 fps: approximately 1.54 milliseconds.

 

[Swedishsteel]

Just how long does it take a car to get to a quarter of a mile?

Enjoy the noise while it lasts. Production run electric cars can now turn a quarter mile in under 11 seconds. Within 5 years internal combustion powered quarter-milers will be competing with an asterisk and a handicap against mass produced electric sedans.

 

[bmcgilvray]

Yeah, but I don't want an electric car. Don't care about performance claims. We travel lots of long stretches of road and I want to be able to gas up rather than to have to recharge.

Electric cars and plastic guns are for a later generation, not me.

 

[gasmitty]

Yeah, but I don't want an electric car. Don't care about performance claims. We travel lots of long stretches of road and I want to be able to gas up rather than to have to recharge.

Electric cars and plastic guns are for a later generation, not me.

As a freshman in college in 1968, my first physics prof asked the class to tell him about themselves. When it came to me, I mention that I liked working on cars and he responded "ah... so you're an antiquarian." This from a guy who drove a smoky, 3-cylinder, 2-stroke Saab 96. (Don't get me wrong, my first new car was a 1980 Saab 99, but Dr. Charlie Miller was a bit off the charts. Ahead of his time in some ways, but vastly behind in others.)

 

[Nmuskier]

@gasmitty your formula is fine. You don't need to worry about an acceleration curve. You calculated the average acceleration and that's all that is needed to answer the question of time.

All that window dressing in the OP about lans and groves etc adds to the complexity of a simple question too.

 

[Tangle]

@gasmitty your formula is fine. You don't need to worry about an acceleration curve. You calculated the average acceleration and that's all that is needed to answer the question of time.

All that window dressing in the OP about lans and groves etc adds to the complexity of a simple question too.

He calculated average velocity, not average acceleration. And, I concur that he did it correctly using constant acceleration. I think we mean constant acceleration, not linear acceleration. The acceleration profile DOES affect average velocity, exit muzzle velocity, and barrel time

For example if the bullet accelerates very fast at first and slower after that, the bullet achieves a higher muzzle velocity than if the acceleration is constant. Although I suspect assuming linear acceleration would be close enough for most of us, if not all of us - if it matters at all.

The easy approach to this is QuickLoad. You set everything up and let it calculate the barrel time. Interestingly enough, QL does NOT take twist rate into account, but it does include barrel cross sectional boral bore area a number of other variables.

That it doesn't take twist rate into account, doesn't seem to be a problem. I ran the same load in Ballistics Explorer, one with a 1:7 twist and one with a 1:9 twist and the muzzle velocity at 250 yards is exactly the same. But...

We can compare QL's calculation to a constant acceleration profile and see if there's a difference - and there will be for the reason I described above.

I used a 300 AAC Blackout caliber fired from a 12" barrel. With 20.0 gr of Lil'Gun powder, a Hornady 110 gr VMAX would leave the barrel in 733 uS (micro seconds). Calculating with constant acceleration and average velocity, we would get a barrel time of 898 uS. That's a difference of almost 23%.

What really happens is the powder burn rate and increase in barrel volume behind the bullet as it travels down the barrel create a non-linear acceleration. Here's what the timing looks like in QL (the velocity profile is the blue trace, the time is the bottom axis.):

Here we can clearly see the acceleration is not linear nor constant. And from the above example calculations That the acceleration profile does make a difference. I think it would be safe to say that the actual barrel time will always be shorter than would be indicated by a constant acceleration approximation.

But then, I have to add, so what? How could we use barrel time any better than the the parameters we have been using for years?

 

[JohnLloydScharf]

Classic case of overthinking.

No. It takes long enough that the barrel can rise before the bullet leaves the muzzle.

 

[Bad Bob]

No. It takes long enough that the barrel can rise before the bullet leaves the muzzle.

I don't know about that. The bullet is well clear before anything happens.

 

[gunenthusiast]

If you really really like differential equations ...

They will be in partial derivatives, and non-linear definitely...

 

[JohnLloydScharf]

I don't know about that. The bullet is well clear before anything happens.

It only takes a fraction of a degree which is imperceptibly as a change in aim in that video. It changes point of aim by as much as 3 inches at 25 yards. You do the math. It does not need to change one MOA if your target is the medulla oblongata from a rifle at 57 yards. It is called bullet dwell time and is just one microsecond from the time the ignition begins until the projectile leaves the muzzle. Recoil is measured in velocity as well as foot pounds of energy. It is the reason people use bull barrels for increasing accuracy. A heavier barrel does not stop the rise, but the energy needed for the inertial of the barrel rise is higher with more mass. It is the reason barrel harmonics is an issue.

 

[since9]

Prove it.

Already did. You weren't paying attention?

 

[since9]

As a freshman in college in 1968, my first physics prof asked the class to tell him about themselves. When it came to me, I mention that I liked working on cars and he responded "ah... so you're an antiquarian." This from a guy who drove a smoky, 3-cylinder, 2-stroke Saab 96. (Don't get me wrong, my first new car was a 1980 Saab 99, but Dr. Charlie Miller was a bit off the charts. Ahead of his time in some ways, but vastly behind in others.)

Did Charlie believe that people who failed to maintain their cars were futurians?

 

[since9]

I don't know about that. The bullet is well clear before anything happens.

Might look that way, but if you play the YouTube video back at 0.25 (quarter) speed, especially on a 40" monitor, you can clearly see the first rise occurring before the round leaves the barrel.

Fortunately, modern engineering has long left the old, Mark I Eyeball in the dust. These days we use things like lasers, mirrors and other means of measuring both fore and after barrel positions, along with barrel rigidity, flex, wobble, warp, compression, elongation and and other spaghetti-like effects throughout the firing sequence, and at FPS far higher than 70k.

In fact, "Called T-CUP, the camera can capture a mind-boggling 10 trillion frames per second."

Alas, that's probably way out of the price range for photographing a gun firing, but cameras a million times slower, way down into the 1 million FPS range, work just fine:

Check about 1:47 and use the 0.25 speed. You'll see the front of the weapon bend down considerably as the rear end of the barrel goes backwards and up.

Thing of it is, so long as all that wobbling is consistent, when you sight it in, you're averaging out all those errors.

 

[bmcgilvray]

As a freshman in college in 1968, my first physics prof asked the class to tell him about themselves. When it came to me, I mention that I liked working on cars and he responded "ah... so you're an antiquarian." This from a guy who drove a smoky, 3-cylinder, 2-stroke Saab 96. (Don't get me wrong, my first new car was a 1980 Saab 99, but Dr. Charlie Miller was a bit off the charts. Ahead of his time in some ways, but vastly behind in others.)

I remember when these could still be seen on the streets of Fort Worth, Texas. Pretty cool car really.

1960 Saab 96 brochure

Not exactly flash and dash though. Hmmm ... takes longer to go from 0-60 than it does to accelerate through a standing quarter mile. So, at the end of a quarter of a mile it still hasn't reached 60 mph?

Acceleration 0-80km/h (50mph)	14.7 s
Acceleration 0-60mph	24.1 s
Acceleration 0-100km/h
Acceleration 0-160km/h (100mph)
Standing quarter-mile	22.3 s
Standing kilometre	39.7 s
Maximum speed	127 km/h (79 mph)