A Look at the Berger Hybrids --- BC, MV, and Wind Deflection

[Joe Grad]

All,

Bryan's approach in his book is to minimize the "non-deterministic" variables of shooting, the most important being wind deflection. He shows that a bullet's wind deflection is directly proportional to lag time, and lag time is determined by a bullet's MV and BC.

I've graphed the bullet curves of 4 Berger hybrids, 0.338, 7mm, 6.5mm, and 6mm in a steady 10mph wind. Using the "Applied Ballistics" online calculator one can find wind deflection directly for each bullet. The average maximum MV's of different cartridges were also placed on the curves to show their relation to each other.

The chart can be used to get a feel for "lag time equivalents". Points on the same horizontal have the same wind penetration ability, regardless of weight and caliper!!! I think this is a good approach for finding equipment that minimizes lag time/wind deflection, regardless of caliper. The Y-axis was inverted so the more north you go on the graph, the lower the wind deflection.


NOTE: The chart says nothing of bullet stability, barrel wear, etc. Also, the MV cartridge values shown are AVERAGES of the Max MVs of all the different powders shown in the Berger reloading manual and may be much lower than what you are getting with your personal loads. They are better used as a relative guide. If you know the MV of your own rifle, just place it on the bullet curve and see where it lands.

 

[Joe Grad]

Here is a different format if you can't download a pdf on your phone...

 

[CharlieNC]

Nice plots Joe. Looking at this in a similar exercise, I also noticed that a basic relationship held closely (not perfect) across a wide range:

Drift =f ( BC x Muzzle Velocity )

I would be interested to know if the same simple relationship appears to hold for the cases you generated.So if you calculated BC x MV and made a plot it should pretty much be a single line.

 

[Joe Grad]

Charlie,

Since G7 BC is constant, I would expect your equation to be linear. I think that the non-linearity you see on the bullet curve has much to do with how the drag coef. changes as the bullet velocity changes over the trajectory.

You might try plotting the curves in excel to see if it's a good fit. I used the applied ballistics calculator with varying MVs. Make sure to set the zero distance the same as distance to the target. This allows you to isolate the wind deflection by excluding spin drift and coriolas.

The classical derivation of wind deflection is....

Tlag = TOFa - TOFvac

where:

Tlag = lag time (in seconds)
TOFa= actual time of flight in seconds
TOFvac=time of flight in a vacuum (no air)

and...

Wd = 17.6 * CWS * Tlag

Where:

Wd= Wind deflection (in inches)
CWS = cross wind speed (mph)

thus...

Wd= 17.6 * CWS * (TOFa - TOFvac)

This is essentially saying that the "wind exposure time" can be thought of as the slice of travel time that is in excess of the vacuum time. If the bullet flies for 3 seconds on the range, but only 2.5 seconds on the moon, then the "wind exposure time" is 0.5 seconds. If the wind is blowing at 5mph or 88 in./sec (5mph is converted to in/sec by multiplying by the conversion factor 17.6), then the wind deflection is 88 in/s*0.5sec = 44 inches...

Wd = (17.6 in.hours/sec.miles) * 5 miles/hour * (3.0 - 2.5)sec. = 44 in.


To dig a bit deeper, you can approx TOFvac by assuming a flat trajectory..

TOFvac = D/MV

where:

D = Distance to target (feet)
MV= Muzzle Velocity (fps)

therefore....

Wd = 17.6 * CWS * (TOFa - D/MV)

Finding actual time of flight is a bit messy, and I would have to brush up on my physics to go further. The applied ballistics calculator will solve for it directly. It also solves for deflection directly, which is what I graphed. Like the vacuum time of flight, TOFa should increase with distance, decrease with increasing MV, and decrease with increasing BC.

Bryan Litz's book explains lag time better than I can.

Hope this helps..

-Joe

 

[CharlieNC]

Joe, not trying to calculate this directly since there are plenty of good ballistics programs for this. When looking at this as you did at a given distance and atmospheric for a range of calibers, weights, and velocities I thought it was very interesting that there is an excellent correlation between BC x MV with max trans-sonic range, wind drift, and drop. To me this is a simple depiction that bullet weight and caliber don't matter much on their own, only as reflected by BC. Of course this is what you read and to me it was a simple visualization to confirm my own curiosity. I would not say there is any practical use, except if you wanted to compare calibers/loads off-the-cuff then the BC x MV is a direct, simple means to judge which is better. And for my geography, interestingly the max trans-sonic range is close to G1 X MV. Such trivia to induldge idle time.

 

[Terry]

The 6 Dasher velocity should be 3,000fps.