Slope Dope

by Fred Ray on December 1, 2008 · 0 comments

Whaaa? Bear with me, we’re not talking about something really exotic here. Consider the following account from the Battle of South Mountain (Boonesboro for you Confederates). The report is from the the 107th Pennsylvania, part of Duryea’s brigade, which was attacking up a steep slope toward Turner’s Gap against Robert Rodes’ Alabama brigade.

in compliance with orders from General Duryea, formed in line of battle near the foot of the hill, and gave orders to move forward with fixed bayonets. Nothing could exceed the promptness of both officers and men in the execution of this order; with enthusiastic cheers they dashed forward, and soon the enemy were scattered, and in much confusion were flying before us. Several times they rallied, and once in particular, having gained an admirable position behind a stone fence, they appeared determined to hold on to the last. Here it was they sustained their greatest loss. Colonel Gayle, Twelfth Alabama, fell dead, and the lieutenant-colonel Fifth South Carolina wounded and taken prisoner. Their stand at this point delayed not the onward movement of the One hundred and seventh a moment, but in a little while we were over the fence and among them, taking 68 prisoners, killing and wounding quite a number, and causing the remainder to fly precipitately to the top of the mountain. … In this engagement we lost 3 men killed and 18 wounded. This small loss is accounted for by the fact that the rebels, being all the while located above us, shot too high. In evidence of the truth of this statement, our colors were completely riddled, while the color-bearer was in nowise injured.

It was obviously the color bearer’s lucky day, but I’ve always wondered why the Alabamians, who were experienced soldiers by this point, shot so high. Had they connected with the Pennsylvanians, they might have held their positions. Turns out they were defeated by a little-known bit of ballistics called slope dope.

In plain language, if the ground slopes down noticeably, there’s a difference between the slope distance i.e. the actual distance from you down to the target, and the horizontal distance, which is measured straight out from your position to a point directly above the target. The two distances form a triangle with the long leg on the bottom.

What this means to you is that if you set your sights at the slope distance, which is the most logical thing to do, the bullet will fly high, just as it did with the musket balls of the Alabamians. You have to use a correction table, or failing that, estimate the horizontal distance to the target. Nowhere have I seen this mentioned in a 19th Century marksmanship text, but I have seen several examples of soldiers shooting downhill who fired high. Now I know why, and so do you.

The sharpshooters of the Twelfth Alabama were on a different part of the field and put effective fire on the Pennsylvania Bucktails, so maybe they knew something about it.

If you want a more detailed discussion of this phenomenon, take a look at this message board discussion, and see Section 3-1 in FM 23-10 (you’ll have to scroll down about three-quarters of the way down the page).

UPDATE: Bill Adams passes on an article by Bob Spencer (scroll down about halfway to the Incline Angle section) that explains the phenomenon very well in plain English:

Think uphill and downhill shooting. There is a built in error in accuracy when shooting either uphill or downhill at steep angles. This cannot be avoided, but can be compensated for. It affects all guns, black powder and smokeless. It isn’t caused by misjudging the distance, it occurs even when shooting over carefully measured distances. The effect can be large enough to cause a miss on a fairly large target at longer ranges. The effect gets worse as velocity decreases and as distance to the target increases. It also gets worse as the ‘incline angle’, the steepness of the slope, increases. Presented with a shot up or down a very steep slope, with a slow moving bullet and at maximum range, we are in deep trouble.


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