Another question on OBT

[mbohuntr]

Not wanting to hijack the last thread, I started a new one...

Hello all, Just joined after lurking at the website, and reading chris's paper on OBT. My math is probably off, but I have a 24" barrel, but the fastest time offered in his table is .816mS.

My version of the math tells me this converts to 2451fps. Am I wrong, or if not, where do I find the nodes for faster or smaller bullets?

Thanks,
Mike

 

[Twoboxer]

. . .where do I find the nodes for faster or smaller bullets?

Thanks,
Mike

http://www.the-long-family.com/optimal barrel time.htm has a link to download an Excel worksheet by Johann Yssel that will calculate nodes for any barrel length. If you don't have Excel, you can probably download and use Open Office Org's free version called Calc instead. You may have to enable editing depending on your security settings.

 

[JasonT]

Remember that the bullet is accelerating from a dead stop until it reaches the muzzle. So it's not just speeding along at 2500fps the whole time.

 

[Twoboxer]

As JasonT points out, most bullets will spend a "lot" more time in a 24" barrel than 0.816ms.

An example from Quickload: 30-06, 24" barrel, 175gr TMK, MV = 2730fps, Barrel Time = 1.226ms.

 

[mbohuntr]

Figures...I hated physics. So if I'm understanding you guys correctly, OBT is the node locations, but actual barrel time is a function of mass x acceleration x coefficient of friction... And the calculator figures dwell times based on those parameters??

I was hoping to be able to roughly estimate accuracy nodes for various bullets of the same grain weight by simply working up the chronograph speed fairly close to the muzzle velocity of a similar grain projectile, then shooting three shot groups at grain increments till I get the sweet spot.

I'm only looking to shoot steel at distance, and hunt, not compete, so I was looking at stuff in the 168s and 125s

 

[FeMan]

Figures...I hated physics. So if I'm understanding you guys correctly, OBT is the node locations, but actual barrel time is a function of mass x acceleration x coefficient of friction... And the calculator figures dwell times based on those parameters??

I was hoping to be able to roughly estimate accuracy nodes for various bullets of the same grain weight by simply working up the chronograph speed fairly close to the muzzle velocity of a similar grain projectile, then shooting three shot groups at grain increments till I get the sweet spot.

I'm only looking to shoot steel at distance, and hunt, not compete, so I was looking at stuff in the 168s and 125s

Since the force applied to the bullet as it goes down the barrel (the pressure) is not constant, then acceleration is not a constant either. Anyone who can really calculate the barrel travel time on paper should be the Nobel Prize! Don't feel bad.

Give me your load data, MV, and barrel length and I'll run it through QL for you.

 

[RonAKA]

I was hoping to be able to roughly estimate accuracy nodes for various bullets of the same grain weight by simply working up the chronograph speed fairly close to the muzzle velocity of a similar grain projectile, then shooting three shot groups at grain increments till I get the sweet spot.

I suspect you will find that the sweet spot is velocity dependent, and within reasonable limits not bullet dependent. Here is a graph of the Ladder Test sweet spot in my 6BR, with Ladder Test results plotted for three different bullets on the same graph. The sweet spot is essentially the same for all three bullets - 3400-3420 fps.

I think the only accurate way to determine the sweet spot velocity is to do a real Ladder Test, and ideally plot the vertical POI vs velocity. You are looking for a flat spot where velocity increases, but vertical POI does not.

 

[mbohuntr]

Since the force applied to the bullet as it goes down the barrel (the pressure) is not constant, then acceleration is not a constant either. Anyone who can really calculate the barrel travel time on paper should be the Nobel Prize! Don't feel bad.

Give me your load data, MV, and barrel length and I'll run it through QL for you.

 

[mbohuntr]

Thank-you! I just picked up the rifle, Savage 10 flcp - sr .308 with a 24" barrel. I probably won't get set up till spring, as the snow is already deep, and the range is closed for hunting season. I will take you up on your offer this spring! THANKS EVERYONE!

 

[kvd]

Figures...I hated physics.

Physics is your friend – don’t be scared!

One may find the average dwell time in a given barrel length by using the two equations for calculating the acceleration of an object if you know the initial and final velocity and the distance or time for the change in velocity. The two equations are:

aavg = (Vfinal – Vinitial)² ÷ 2L, and aavg = (Vfinal – Vinitial) ÷ (tfinal – tinitial); where V is velocity; L is distance (in our case, the barrel length); and t is time in seconds

I say average because we don’t really know what is going on in the barrel from the time the bullet just starts to move until it exits the crown. We only know that we pull the trigger and shortly thereafter the bullet leaves the barrel with a certain speed that we call muzzle velocity. To give an example of how to solve for average barrel dwell time, say one has a 29 inch barrel and the bullet has a measured MV of 2900 ft/sec. Substituting these numbers in the first equation:

aavg = (2,900)² ÷ 2(29 ÷ 12) = 1,740,000 ft/sec² . We assume Vinitial is zero ft/sec so it is dropped from the equation.

Using aavg from the first equation and solving for time in the second equation above (assuming Vinitial and tinitial are zero) we end up with:


t = 2,900 ÷ 1,740,000 = 0.00167 seconds or 1.67 milliseconds.


Not sure how this aligns with the values returned from Quick Loads – having never used the program. Hope this is of use.


Ken

 

[BenPerfected]

Being mathematical challenged, I'll just stick to slightly adjusting my tuner.
Ben

 

[FeMan]

0.00167 seconds or 1.67 milliseconds.


Not sure how this aligns with the values returned from Quick Loads – having never used the program. Hope this is of use.


Ken

Impressive Ken! Quickload gives 1.278 ms as the travel time. The max acceleration is reached at 1.3 inches of travel and bleeds off from there. Not at all a linear acceleration.

 

[mbohuntr]

Physics is your friend – don’t be scared!

One may find the average dwell time in a given barrel length by using the two equations for calculating the acceleration of an object if you know the initial and final velocity and the distance or time for the change in velocity. The two equations are:

aavg = (Vfinal – Vinitial)² ÷ 2L, and aavg = (Vfinal – Vinitial) ÷ (tfinal – tinitial); where V is velocity; L is distance (in our case, the barrel length); and t is time in seconds

I say average because we don’t really know what is going on in the barrel from the time the bullet just starts to move until it exits the crown. We only know that we pull the trigger and shortly thereafter the bullet leaves the barrel with a certain speed that we call muzzle velocity. To give an example of how to solve for average barrel dwell time, say one has a 29 inch barrel and the bullet has a measured MV of 2900 ft/sec. Substituting these numbers in the first equation:

aavg = (2,900)² ÷ 2(29 ÷ 12) = 1,740,000 ft/sec² . We assume Vinitial is zero ft/sec so it is dropped from the equation.

Using aavg from the first equation and solving for time in the second equation above (assuming Vinitial and tinitial are zero) we end up with:


t = 2,900 ÷ 1,740,000 = 0.00167 seconds or 1.67 milliseconds.


Not sure how this aligns with the values returned from Quick Loads – having never used the program. Hope this is of use.


Ken

OK... Plugging in 2600fps out of a 24" barrel gives you 1.54mS, past node 7 on the table???? please check my math, but everyone says this is near a node...

 

[FeMan]

OK... Plugging in 2600fps out of a 24" barrel gives you 1.54mS, past node 7 on the table???? please check my math, but everyone says this is near a node...

That equation does not accurately predict barrel time. You should end up between nodes 4 and 5 depending on what powder and bullet you choose.

 

[kvd]

Not at all a linear acceleration.

Very true. As I indicated, we can only determine the average acceleration and average dwell time in the barrel with these equations. I’m sure the accelerations is changing within the barrel. However, I would question the statement that maximum acceleration is reached at 1.3 inches into the barrel and the bullet is decelerating passed that point. Maximum muzzle velocity would be obtained at the point of maximum acceleration – so should we be using rifles with 1.3 inch barrels?

Some of the graphs I’ve seen posted on this site that were produced by the QL program seem to suggest that the pressure spikes very soon in the propellant burning reaction and falls off within a few inches of barrel travel. Yet it also shows the velocity continuing to increase on another axis. Clearly, if the force – in this case a pressure gradient – is decreasing, the bullet will be decelerating – not accelerating as indicated by QL. Velocity would not be the correct parameter to put on the right axis. Velocity is constant change in displacement with respect to time. Change in velocity with respect to time is called acceleration/deceleration as the case may be. In truth, a bullet never really has a velocity in its travel but is ever accelerating and decelerating from the time the propellant starts to burn until it hits something solid and stops. So unless I’m not understanding what is being presented, I’m compelled to question the QL graphs with pressure on the left hand axis, barrel length along the bottom axis and velocity along the right hand axis.

Plugging in 2600fps out of a 24" barrel gives you 1.54mS, past node 7 on the table???? please check my math, but everyone says this is near a node...

As you can see, the arithmetic is straightforward. If one starts at zero velocity (and by definition zero acceleration) and reaches a certain velocity in a given distance then the average acceleration must be “X” ft/sec². Knowing the average acceleration and the velocity it produces, one can determine the time the acceleration acted for in seconds. This is not telling you OBT and is not dependent on the mass of the object.

Ken

 

[mbohuntr]

It is starting to appear that due to the multiple variables involved such as different burn rates, different shaped bullets, different copper/lead alloys, lubricants, barrels etc, (even the coefficient of friction is no longer a constant because copper is shed as the bullet travels down the barrel.) You can come close to the node with the program, but not precisely.
I think you still need ladder testing to pinpoint the exact speed and seating depth given your setup. Does anyone using the program have anything to add?

 

[dmoran]

....The max acceleration is reached at 1.3 inches of travel and bleeds off from there. Not at all a linear acceleration.

Think you have it confused, and are actually referring to pressure. Max acceleration takes place after peak pressure, to barrel exit. It is the pressure behind the bullet that "bleeds off" after peak pressure. The bullets continue to accelerate the entire length of the barrel.
Donovan

 

[RonAKA]

Think you have it confused, and are actually referring to pressure. Max acceleration takes place after peak pressure, at barrel exit. It is the pressure behind the bullet that "bleeds off" after peak pressure. The bullets continue to accelerate the entire length of the barrel.
Donovan

Acceleration is the rate of change of velocity. Peak acceleration can occur at any velocity, and I suspect does occur when pressure is at maximum. While velocity continues to increase as the bullet goes down the barrel, acceleration is decreasing.

 

[JLT]

Think you have it confused, and are actually referring to pressure. Max acceleration takes place after peak pressure, at barrel exit. It is the pressure behind the bullet that "bleeds off" after peak pressure. The bullets continue to accelerate the entire length of the barrel.
Donovan

You're both correct, depending on context. In almost all cases, a bullet will continue to accelerate the entire length of the barrel - the first derivative of velocity. The second derivative of velocity - the rate of change of the rate of change - begins to diminish after peak pressure is reached.

Physics is indeed your friend . . . and so is differential calculus. Can't have one without the other.

 

[RonAKA]

You're both correct, depending on context. In almost all cases, a bullet will continue to accelerate the entire length of the barrel - the first derivative of velocity. The second derivative of velocity - the rate of change of the rate of change - begins to diminish after peak pressure is reached.

Physics is indeed your friend . . . and so is differential calculus. Can't have one without the other.

Yes, I agree, and maximum acceleration is certainly not at the muzzle. Force = Mass X Acceleration. Force in a gun is the pressure. The mass of the bullet does not change. So when Force (pressure) is highest, the acceleration has to be highest.