Friends,
for the folks in the "know" ,I would like to learn about ballistic tables to be used in the mountains,meaning distance adjusted for angled shots.I understand the difference to horizontal are significant and of course increase with distance,such that a "well placed shot" for 300-400 yards out would miss completely because of a 30-40 degree angle.I remember having heard that one should take the underlying horizontal distance for selection of the drop chart,but the logic is not readily evident to me.

thanks for enlightening me and us

sheephunter

It's math & gravity. If you range an animal on a steep up/down hill & it is 442 yds on a 45deg slope, he is actually only 300yds away. If you are sited on @ 300, you should hold on. If you hold for 450yds you'll shoot over.
The bullet travels in a line & falls @ the same rate whether you shoot up, down or straight. It's that geometry equation, Pethagorams (sp) theory for finding the daig. of a triangle. Just remember that if you are shooting @ an exteme up/down the animal is closer than he appears. You want to aim on or low depending on your zero.

Imagine shooting straight up or down. In this case, there will be no "bullet drop", only a slight increase or decrease in the bullet velocity when compared to a round fired horizontally at the same distance.
Thats how I picture it. Horizontal distance gives you the bullet drop. Vertical distance gives you a change in velocity.

Go to huntingnut.com and download pointblank. It lets you put in elevation numbers, and thus while away many hours playing "what if". FWIW, Dutch.

Thanks for the show of support folks.As I indicated ,I am aware that sloped shots should be taken as "shorter distances" than measured as gun to target.I am interested in a more precice determination - dont know what it will yield but cant hurt to look at the math.I understand the long distance shooters have different drop tables for the bullet path.I E mailed Dallan who unselfishly writes the PointBlank program so many of us use and he told me that so far he has been unsucessful to calculate the "adjustment" for angled shots.So I thought the combined brain power of this forum got to produce the proper formula or 2nd approximation for it.
Dutch ,I cant see a facility in PontBlank to play with this scenario like you suggest,PoinBlank allows to dial in the altitude,but thats still for level shots if thats what you are referring to,if not please could you tell me where one can get an idea of above.

thanks

I am holding my breath for the math inspired individuals

sheephunter

To help this topic along - maybe.I heard the same theory that OldFart outlined: the horizontal distance underlying the angled shot determines the bullet drop.I like his analogy of a shot straight up : bullet drop zero.
I just have a grinding noise in my brain to understand why that is so,not for the straight up shot,I even understand the straight dn shot
but for lets say the 40 degree shot.

Buut,if that theory is accurate the problem is solved ,as the horizontal distance to target can be calculated from the angled distance and the tangent of the slope.

I - we - just need some solid minds here that would confirm this theory

sheephunter

Sorry, correction,
its not the tangent but cosine that would yield the underlying horiz distance to target.I just calculated that a 45 deg shot at 300y would only be 212 yard for bullet drop.That is significant.

sheephunter

Sheephunter

Using the Cosine of the Line-Of-Sight (LOS) angle is the correct answer, partially. It's been a while since I've reviewed this subject but here goes anyway.

There are two (2) basic schools of thought (as I've found) on the "problem". You can apply the cosine of the LOS angle to the measured LOS distance to the target or you can apply the cosine of the LOS angle to the trajectory "drop" for the measured (LOS) distance. Some folks are firm believers that the cosine should be applied to the trajectory "drop" value, make the correction and shoot.

The problem becomes more apparent when we examine Time Of Flight (TOF) for the projectile. TOF for the 300 yards of your example LOS distance for a 308 round is about .372 seconds...TOF for a round traveling only 212 yards is about .26 seconds. The round still must travel an additional .11 seconds to get to the target...the trajectory is effected by this additional .11 seconds as the projectile's speed is decreasing and the overall "drop" increased with the added TOF. It's only a small difference between the two methods for the distances you're discussing but it makes for a difficult situation at longer ranges and/or when shooting small (precision fire) targets.

One thing that is clear is that the wind component remain fixed at the LOS distance value. The angle to the target may be 45 degrees and the new trajectory "drop" values may be less BUT the windage requirement remains the original LOS distance (uncorrected).

An example:

308 Win
175 Grain Sierra MK (BC .508)
Muzzle velocity: 2700
STP
Sight Height: 1.75"
Zero Distance: 100 yards

Trajectory
300 yards, no slope

13.7" total drop, 4.4 MOA correction required TOF .372 sec.

300 yards (LOS), 45 degree slope

Cosine to LOS distance = 212 yards

Using the new LOS distance to calc drop.
4.4" total drop, 2.0 MOA correction required (TOF predicted for this "corrected" distance is only .251 sec.)

Using the cosine value and the "drop" for a horizontal TOF of .372 sec. (300 yards)
9.7" total drop, 3.1 MOA correction required.

There's more to the entire problem than I describe here...that's probably why there's some controversy about the entire affair.

Here's a relatively new website article about inclined fire. Lengthy and I haven't read the entire article but it appears it discusses the two general methods and offers a third compomise.

http://www.51phantom.com/ebexplained/article1.html

Maybe this link will stay alive longer... same article...

http://www.exteriorballistics.com/ebexplained/article1.html

[ 07-31-2003, 01:22: Message edited by: David King ]

Interesting thread on the subject @:

http://www.thehighroad.org/showthread.php?s=&threadid=27557&highlight=slope+doper

The slope doper mentioned seems an expedient way to cut a few corners. It is shown on pg. 16 of the Aug. 2003 American Rifleman magazine.

Regards,
hm

Far too lengthy for me to type in here but if you want to crunch the numbers and get a definitative explination, you'll find the formulas and tables you're looking for in your "Reloading Manuals" !!

Also Sierra has launched a New web site;
Catering to those interested in more technical exterior ballistics data and information:

www.exteriorballistics.com on June 15. 2003

Technical information from both the 4th and 5th Edition reloading manuals as well as the entire Exterior Ballistics tables from the 4th manual are present on the site. A question and answer message board will keep you informed. Technical articles from Sierra Ballistic Experts Ted Almgren and Bill McDonald as well as the Sierra Ballistic Technicians

Thanks folks,all enclosed links are very helpful
I understand that the topic sounds esoteric to flatlanders shooting a deer at 50-200y,but that is not my real world situation.Even an approximation of correct bullet drop is essential if one wants to hit a target in steep inclines.Much appreciated reading

thanks
sheephunter

Imagine shooting the target with your range finder, this distance will be your direct distance and aka your hypotenuse. The formula for finding the horizontal distance to target is hypotenuse * cosine(shooting angle). The angle being the angle between your hypotenuse and horizontal component line. Doesn't matter if you're shooting up or down. This horizontal component of the distance is where gravity will affect the bullets flight for the duration of the time to the target. Quite simply I believe if you're shooting at what is a significant angle, make a rough calculation and shoot at the target as if you were shooting at it placed at your calculated horizontal component distance. This has probably already been said but I skimmed the other posts and thought I'd put it in my own words.
Good shooting,
Conrad

Kind of a mute piont unless your shooting over 300 yds -isn't it? And since most game is shot at 100-150 yds it makes this an even less of a thing to worry about as the changes in trajectory are very minimal at best, (always High) not lower. So if your shot at 45+/- your going to be a 1/2" higher then if it was a flat shot! And the problem is?

[ 08-02-2003, 01:29: Message edited by: Gunnut45/454 ]

Gunnut45/454

As I review the original post I come across a few points you apparently missed...

...for the folks in the "know"...

I would like to learn about ballistic tables to be used in the mountains,meaning distance adjusted for angled shots.I understand the difference to horizontal are significant and of course increase with distance,such that a "well placed shot" for 300-400 yards out would miss completely because of a 30-40 degree angle.

Gustavo

Thanks for offering a bit of info...

When you do sight height, something I haven't messed with, how is it applied? It seems there are at least two (2) problems to deal with in the inclined fire problem.... sight height being the one I've recently been considering. I began considering this when working on a problem for rifle "cant" error...just didn't continue with the problem toward a solution/understanding.

If I shoot my rifle (zeroed at 100 yards) with a sight height of 1.75 inches I build into the system the Time Of Flight "drop" to 100 yards AND as I understand it this will include the Sight Height component. BUT, if I then shoot the rifle straight down OR straight up I'll have an angular error equal to the sight height (1.75 inches but due to the 100 yards zero it's probably more correctly stated as ~1.75 MOA). This problem became evident (as I understand it) when working on the "cant" error. Sight a rifle at 100 yards (scope height 1.75 inches) then rotate the rifle 90 degrees and fire onto the target... the rounds printed ~3.75 inches low and of course left or right ~3.75 inches depending on the direction of the rifle rotation chosen (more than the ~2 MOA expected).

So... do I remove the sight height component by the cosine value independently or should I give it a little more thought?

I have a trip to Colorado this fall and plan to test (actual field test...semi controlled) some inclined fire. Long Range shooting and this little problem seem to go hand-in-hand.

/r

[ 08-03-2003, 05:43: Message edited by: David King ]

This is a quote from an article by Dan Lilja.

Shooting uphill or downhill will result in high shots if the angle is roughly 15 degrees or more or if the range is very long for lesser angles. The actual bullet drop is dependant on the true horizontal distance to the target not the slant range. Our range finders measure the slant range. Again there are several methods to determine the amount of correction necessary. Most, if not all, ballistic programs can take into account angled shooting and print out the correct drop for any range. The Sierra handloading manual in the exterior ballistics section deals with this subject with an example.

The Sierra manual has a table of factors that in use are multiplied by the total drop in inches, for the slant range to the target. The factors are .034 for 15 degrees, .134 for 30 degrees, and .293 for 45 degrees. There are more listed in the manual but these will give the reader an idea of the degree of change as the slope increases. Their use is simple. Let's say that you were looking uphill at a mule deer buck that your range finder said was 675 yards away. Looking at your drop chart you read that for that distance you need 11 1/2 minutes of adjustment in your scope. The catch though is the buck is uphill at an angle of 30 degrees. Using these factors we take the total drop for 675 yards (which is 103.1 inches) and multiply by .134 (the factor for 30 degrees) and the result is 13.8. That is to say that the bullet would impact about 14 inches high if we did not allow for the angle. Fourteen inches is about two minutes of angle at that distance. From this example we can see that it would be easy to miss that buck had we not taken into account the steep angle to the deer.