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Hard Sums!


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So this week I added a new 'weapon' to my long rang plinking arsenal... A GPS device. (I'm using a Garmin Montana 650T - Ruggedised Weather Proof GPS that I use on my motorbike!)

 

I used to use a Leupold Range Finder, supposedly accurate up to 1,000 yrds... It defiantly wasn't any use trying to range a 20" gong.

 

Whilst setting up the gong I can use the GPS to set it as a 'way point' then move back to my shooting position and let the calculations begin.

 

My Ballistic App of choice is Strelok Pro and to give me the best chance of a hit, I like to be as accurate as I can with the information I enter in.

 

Life was easy with the RF. I'd point it at my target, and if it could range the target it would tell me the range and the angle to the target.

 

No such luck with the GPS. It will give me a pretty accurate distance as the crow flys and it'll give me the elevation of my waypoints and current position, the rest is up to the GCSE Math I learned at school... Trigonometry.

 

So just for ease, the following is a very close example of one of my shoots... I've just made the numbers concerned a bit rounder!

 

GPS distance to target = 1,000 yds (3,000ft)

GPS elevation of target = 200ft

GPS elevation of shooter = 700ft

 

If the shooter and target elevation are close enough I can forget all of this, but since this is not the case for me I always find that my distance to target is further than the GPS claims.

 

First to get the unit measurements you need.

 

Elevation difference: 700 - 200 = 500ft

 

GPS distance to target : 1,000 x 3 = 3,000ft

 

Next to work out the shooting angle (a) ...

 

a = 500 / 3,000

 

a = 0.16666667 (tan-1)

 

a = 9.46232

 

So I can choose to input -9 or -10 degrees (because I'm shooting down to the target) into my ballistics calculator.

 

Now to work out my actual distance to target (d) ...

 

d = (500x500) + (3,000x3,000) = 9,250,000

 

d = √9,250,000 = 3,041

 

d = 3,041 / 3 = 1,013

 

Actual distance to target = 1,013 yds

 

I know what you're thinking... What's 13 yrds between friends!

 

No? That's right, because what you're actually thinking is "Just download a Trigonometry App!"

 

Don't worry, I have... I just like to know that if needs must! :-)

 

Jay.

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Jay,

 

You're a man after my own heart. Why solve a problem a simple way when there's a longer method?

The trouble is that if you're a maths geek (and I'm in that camp) doing the trig is just plain fun.

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just make a best guess and have at it !

That's what I'd do, the angle compensates somewhat for the extra range, total error looks like about 5" for my rifle as calculated by Strelok, unless you're shooting at something unrealistically small it shouldn't make a difference.

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Well,it's a couple of inches (always less hold over /clicks up) than the slope distance for any likely slope/stalk range.

 

For longer shots you will need to get it closer: the distance you need to adjust for is pragmatically given by the line of sight multiplied by the cosine of the angle of the slope.

Major JL Plaster(USAR ret) has obligingly given a table of cosine values, and using that you are just doing one multiplication- you do need the angle of course-some gizmos give it,some rangefinders have it as an option .

The cosine values are in Plaster "Shooting uphill and downhill" google

Having them might just let you get your shot in before the corvid leaves for the next class "Surviving hard sums done the hard way".Bryan Litz,Chuck Hawks,Jim O'connor and indeed every practical authority uses this-it's pretty close.

(note the cosine is less than one ,so your actual ''come up distance-will always be less than the line of sight.Up/downhill makes no difference,it's shorter than line of sight.

 

You can get pretty close with some simple rules (rounding decimals etc) thus:

 

"For a 30 degree slope,target is engaged as if it were 90% of the slope distance"

Which is 'reduce distance by 10%" so the 800 slope shot on a 30 degree slope needs 720 y holdover/clicks.

 

You may well not get a centre hit,but that's because you can't do the sums on the wind!

 

gbal

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Shoot me down if I'm wrong here, but isn't the angle meant to reduce your drop? Ie the GPS distance is your actual distance that you need to use, and 1013 is the figure your rangefinder should show

http://artoftherifleblog.com/angle-shooting-made-easy/2012/09/angle-shooting-made-easy.html

You're right, if the RF can read the distance that is what it would say... I'd then enter that into my balistics program along with the angle it gives me.

 

The whole point of my maths is to find that distance and angle to put into the program. I wouldn't stand a chance at a hit I entered 1000 yrds and no angle!

 

As far as my quarry escaping by the time I'd done the math... Steel tends not to fly or hop away! :-)

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You're lucky it's close enough for a straight line approximation to work, distance between two LLH points on the WGS84 ellipsoid model of the Earth is even more fun!

I hope to one day enjoy such a task! :-)

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Jay,

 

You're a man after my own heart. Why solve a problem a simple way when there's a longer method?

The trouble is that if you're a maths geek (and I'm in that camp) doing the trig is just plain fun.

Funny thing is, I hated it at school and was rubbish at it!

 

Maybe they should of put it in a shooting scenario.

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Well,it's a couple of inches (always less hold over /clicks up) than the slope distance for any likely slope/stalk range.

For longer shots you will need to get it closer: the distance you need to adjust for is pragmatically given by the line of sight multiplied by the cosine of the angle of the slope.

Major JL Plaster(USAR ret) has obligingly given a table of cosine values, and using that you are just doing one multiplication- you do need the angle of course-some gizmos give it,some rangefinders have it as an option .

The cosine values are in Plaster "Shooting uphill and downhill" google

Having them might just let you get your shot in before the corvid leaves for the next class "Surviving hard sums done the hard way".Bryan Litz,Chuck Hawks,Jim O'connor and indeed every practical authority uses this-it's pretty close.

(note the cosine is less than one ,so your actual ''come up distance-will always be less than the line of sight.Up/downhill makes no difference,it's shorter than line of sight.

You can get pretty close with some simple rules (rounding decimals etc) thus:

"For a 30 degree slope,target is engaged as if it were 90% of the slope distance"

Which is 'reduce distance by 10%" so the 800 slope shot on a 30 degree slope needs 720 y holdover/clicks.

You may well not get a centre hit,but that's because you can't do the sums on the wind!

gbal

I'll look up that table, it will be a more than handy reference point... Cheers George.
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You're right, if the RF can read the distance that is what it would say... I'd then enter that into my balistics program along with the angle it gives me.

 

The whole point of my maths is to find that distance and angle to put into the program. I wouldn't stand a chance at a hit I entered 1000 yrds and no angle!

 

As far as my quarry escaping by the time I'd done the math... Steel tends not to fly or hop away! :-)

I shoot on the flat, so this is all theoretical to me, and again, I'm a novice to this. My understanding is

 

1013yds at 10 degree angle = 1000 yards actual? (No angle)

 

Edit: 1013 yards at 10 degree angle = 1000yds of gravity; which is what causes the bullet to drop

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1000 yrds flat dial for 1000yrds

 

1000 yrds from a 10 degree vantage point, actual range is 1013 yards...

 

If the app has the ability to calculate the drop including an angle, then you can enter all the information as you have it...

 

If not and you have to compensate, dial for 1008 yrds... (This is spesific for my bullets and data!)

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1000 yrds flat dial for 1000yrds

 

1000 yrds from a 10 degree vantage point, actual range is 1013 yards...

 

If the app has the ability to calculate the drop including an angle, then you can enter all the information as you have it...

 

If not and you have to compensate, dial for 1008 yrds... (This is spesific for my bullets and data!)

No. The actual range is your horizontal range. Cosine of 10 degrees is 0.98480775301. Therefore effective horizontal range is 985 yards. Regards JCS

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1000 yrds flat dial for 1000yrds

 

1000 yrds from a 10 degree vantage point, actual range is 1013 yards...

 

If the app has the ability to calculate the drop including an angle, then you can enter all the information as you have it...

 

If not and you have to compensate, dial for 1008 yrds... (This is spesific for my bullets and data!)

 

so if you took best guess (as you have to with wind) and 'had at it' with your sights set for 1000yds you'd hit your 20" gong ?

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Yes JCS, sorry, got my numbers a little back to front... I'm juggling a baby, Frozen on the TV at full belt and trying to do math! :-/

 

One thing I'm now not sure on... If I am to enter my range in to Strelok, do I give my horizontal range of 1000 yards or my actual range of 1013 yards?

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GPS should give your horizontal range? If so...No triangle maths required!

Fair enough... I'll save myself the hassle. I just assumed I need to do the math to get the actual range!

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I'd be among the last to not use math for ballistic solutions,but it has to be correctly applied.Whether you want to reinvent the wheel,and work it out longways,is up to you-and whether your target will oblige.But most of us have ballistic programs to reduce the calculations-it is slower,tedious to most,and liable to error.When shooting up/down a slope the 'actual shooting distance'-what you use for your scope settings is always less than the 'line of sight' distance on the slope.

What that distance is is most easily calculated by the formula:

scope adjust distance is (slope distance X cosine of the angle of the slope).

So in the example used its (1000X cosine 10) which is 1000x.985 ie 985 yards.

You set your scope for a 985 shot.

 

nine and a half degrees would come around 987 y,approx....not doing the cosine here!

 

Note the firing solution distance is less than the slope/RF reading.Always-check.

 

The Quick fix' method is just to round out the cosine values eg 10 degree slope,take off 10%,rather than 9.85....giving 990 yards..very quick,often good enough,error low.

You either remember a few of these percentage reductions for a few slopes. like 5,10 ,15 or if you are going onto something a bit more/less steep look it up in advance.

Accuracy is reckoned to be +/- 2 inches to 600,a bit more at extremes.How big is your gong?

Its fast,which is sometimes needed,and gives a good ball park answer-which is a usefulcheck on more precise calculations,which should be close.

 

The reason is a hoary old chestnut.To say that the bullet is affected by gravity along the horizontal distance' is slightly misleading theory,but does give a very good way of calculating what to do about it (cosine).

If you feel think that 'the vertical vector of g perpendicular to the bullets path,is less than g",then advance to A level ,but it does not really tell you what to do with your sights(well,'adjust less than on the level',I suppose.)

 

This is what experienced ghillies have advised long before ballistic apps: "On a slope,don't hold so high",and failure to take this advice can be rebuked "Wasted into the bl**dy heather"....and for especially poor shots...."somewhere in Scotland". :-)

 

gbal

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GPS should give your horizontal range? If so...No triangle maths required!

 

Agree with that. Equally a good range finder should have the facility to give horizontal range too. I typically park my car at the firing point in order to give me a good sized target to range on.

 

Regards

 

JCS

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