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1. Average your pacecount over 100 yards. For example, I think I personally take 72 steps in 100 yards, if I recall correctly.

2. Shoot an azimuth to the object you want to know the distance to that is off of the line you'll travel in step 3. this is angle 1.

3. Walk any direction except directly toward or away from the object (It's hard to walk unwaveringly toward or away from your object, so don't worry too much about it) and count your paces. The further you walk, the more accurate your distant calculation to object will become, unless you can somehow calculate angles down to the minute and seconds.

4. Use your pace-count to determine your distance traveled.

5. Shoot a second azimuth at your object which is also relative to the line you just traveled. this is angle 2.

6. You now have the length of one side of a triangle and two angles, and can subsuquently solve for all angles and all sides (distances) of an oblique triangle (a right triangle only needs one angle and one side length) using the laws of sine.

7,8,9, and 10. Okay, here goes nothing:

Let's say that your first azimuth was 30 degrees, your second azimuth was 40 degrees, and that you calculated the distance you walked (using your pace count) to be precisely 100 yards, for simplicities sake.

All three angles in every triangle ever made adds up to 180 degrees. So, the missing angle in our fictional triangle = 180 degrees - (30 degrees + 40 degrees), which = 110 degrees.

So, A = 30 degrees, B = 40 degrees, and C = 110 degrees. Line c = 100 yards.

Now that we know all the angles, we can use the law of sines to find the measure of the sides (or the distance to your object) The law of sines says that:

a/sin A = b/sin B = c/sin C

Using these equalities we can see that:

a/sin A = c/sin C

Plugging in the values we know, we get:

a/0.5 = 100/0.9397---------> a/0.5 = 106.4169 -----------> a = 53.2084

Likewise:

a/sin A = b/sin B (you could also use the equality b/sin B = c/sin C)

Plugging in the appropriate values, we get:

53.2084/.5 = b/0.6428 --------> 106.4168 = b/0.6426 ---------> 68.3834 = b

And there you have it.

The starting angle you measured between your unkown-distance object and your projected travel distance was angle A, or 30 degrees. You walked 100 yards (which is the length of side c) and shot another azimuth toward your unknown-distance relative to your line of travel, and it was angle B, or 40 degrees. Using the laws of sine, we found that:

1. When you were standing at the place you took your first azimuth, your distance to your object (line b) was ~68.4 yards.

2. When you were standing at the place you took your second azimuth, your distance to your object (line a) was ~53.2 yards.

This is the best I can do using a text medium. Here is a website that I found which explains it the best. Scroll down to "Law of Sines."

http://library.thinkquest.org/20991/alg2/eqtri.html

It really is a lot easier if you can draw a picture. It seems like a lot to do, but it's relatively quick and simple.

....Three cheers for math! :thumb:

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I'm totally not badmouthing the application of trigonometry in right triangles, but right triangles aren't always available while you're hiking. One thing that IS always available is the ability to hike 100 yards and shoot another azimuth. For this reason, the law of sines is infinitely more applicable in a hiking situation, and only slightly harder to understand. :thumb:thanks, it wasnt too hard to understand

this is alot simpler, just find the tangent

d = (Tan (90 - (A -B))) x Ref

I'll test it on a known distance course as soon as I can to see if it's solid method, but I have to say that 'solve for the tangent' is a more field expedient formula to stick to, especially if you have a scientific calc on hand.

plus the advantage of my way is alot less walking, hence it'd be ideal for a long range marksman.

Correct me if Im wrong here but wouldnt walking 2x farther for the reference distance make your estimation 2x more accurate?

Since your reference (distance walked in a perpendicular direction) is gonna equal the exact width of the stream. You're basically walking until your azimuth reads 45 degrees + the initial reading.

That being said, its meant for someone that has no time to figure out tangents, sines...cosines....(someone entirely without a calculator, working with much smaller distances)

once again, Id opt to do less walking and just figure out the tangent in that scenario.

d = (Tan (90 - (A -B))) x Ref

Im kinda excited to actually test all of this, I may get out of buying a laser range finder. 25-50yd accuracy out beyond 600yds is OK with me. If that aint too optimistic.

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d = (Tan (90 - (A -B))) x Ref is indeed a simpler formula. Just make sure you understand that it only works for right triangles, and you may not always be able to walk perpendicular to your target.

this is alot simpler, just find the tangent

d = (Tan (90 - (A -B))) x Ref

I'll test it on a known distance course as soon as I can to see if it's solid method, but I have to say that 'solve for the tangent' is a more field expedient formula to stick to, especially if you have a scientific calc on hand.

plus the advantage of my way is alot less walking, hence it'd be ideal for a long range marksman.

Correct me if Im wrong here but wouldnt walking 2x farther for the reference distance make your estimation 2x more accurate?

I'm not sure about the ratio of accuracy, but, yes, the farther you walk, the more accurate your reading will be, unless you have some super-awesome instrument that can measure minutes of angle and seconds of angle. :thumb:

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That will find your location on a map, which you could then use to quickly scale the distance to your target. The law of sines works without a map, and is more accurate. :thumb:You guys got it backwards. Stay put and get 2 seperate azimuths back to your position from known terrain points using terrain association and your 7 1/2 minute topo maps(you DO have them don't you?)and do the trig back to your position.

Sine=o/h

Cosine=a/h

Tangent=o/a

Once you have your own position pinpointed it's real easy to get a second reference from another localle to the target and do the trig back again. The real beauty of law of sines is that you don't need right angles.

Regardless of how you do it you still need to be certain of your own position first.

I cant think of many scenarios where I wouldnt be able to walk 10-20 yards (left or right) to get my 2 azimuths to tgt.

Im assuming to get better results when walking perpendicular to the target azimuth I would only have to do a 90 deg. offset. 1st azimuth minus 90 degrees, walk 10yds...shoot 2nd azimuth.

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Just get out there and try both methods out. You'll find out real quick which one is better for whatever your application is.

I cant think of many scenarios where I wouldnt be able to walk 10-20 yards (left or right) to get my 2 azimuths to tgt.

Im assuming to get better results when walking perpendicular to the target azimuth I would only have to do a 90 deg. offset. 1st azimuth minus 90 degrees, walk 10yds...shoot 2nd azimuth.

Redudancy strengthens the resilience of systems. It's better to know more than one way. :thumb:

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I tried this on a couple of occasions. Last time on a known distance range.

If you take 30 steps (10 yards, 7 meters) and multiply the TAN x 7 METERS! it will give you a very very accurate reading at 100 and 200 yds.

Walking 30 steps will give you a 2 degree difference at 200yds and obviously twice that (4 degrees) at 100yds.

So 30ft is good for anything that is 300yds away, what you think is 300yds away....so that in itself is a problem.

So, back to the drawing board with this one:

I was expecting the compass to be moving dramatically but in the end all I got was usually a 2-5 degree difference and the ref dist (the one you walk in a 90 deg. left or right) cant be the same for all ranges.

If you aim in on a 1,000 target with the compass and walk 30ft you might get a 1 deg. difference in your 2 compass readings at point A and point B.

If you walk 7m for a 100yd reading, you need to walk 70m for a 1,000 yard distance.

So realistically you start with a guess and alot of confidence in your compass skills.

Estimate range to target. If you think its a 1,000yds, well you better walk the 70 meters perpendicular to it (or 90 deg left or right from your 1st reading)

By walking 70m between readings, you will get a 4 deg. difference and you will know your target is 1K away.

If your result doesnt agree with your guess.......try 1,100, or 900..

I hope you math wizzes will back me up on this..

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1) Estimate the width of the object you're looking at.

2) Close one eye.

3) Hold your thumb out at arms length, with one edge of your thumb aligned along one edge of the object.

4) Note the position of your thumb relative to the object.

5) Switch eyes (don't move your thumb!)

6) Estimate the distance your thumb moved relative to the object (1.5 thumb-widths? 2 thumb widths?)

7) Multiply the estimated width in step 1 with the number of thumb-widths, then multiply by ten.

Voila! You have the distance.

For example:

Observe a distant car. Estimate the length (if you're looking at the side). Let's say 12 feet. Close one eye, extend your arm, raise your thumb and place it on the bumper. Switch eyes. Note how many thumb-widths your thumb has moved relative to the car. Let's say 3. Multiple 12 feet by 3 (thumb-widths) by 10 = 360 feet away. Voila!

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Estimating how much daylight hours you might have with a thumb makes more sense than trying to estimate something you need precision for like range estimation. Plus the thumb width method will get you 200 meter +/- accuracy at 1,000 meters...

So unless you're a mortarman..

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I can get +/- 5% easy. That's pretty dang good for a <5 second, no equipment required estimation.

Estimating how much daylight hours you might have with a thumb makes more sense than trying to estimate something you need precision for like range estimation. Plus the thumb width method will get you 200 meter +/- accuracy at 1,000 meters...

So unless you're a mortarman..

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