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Testing trajectories in the past

by Tom Gaylord, a.k.a. B.B. Pelletier

Before we begin, here’s an update on my good friend Earl “Mac” McDonald, who’s contributed so much to this blog and has enriched my life and the lives of many who participate here. He’s at home, being cared for around the clock by a home-care nursing staff. That will soon transition into home-based hospice care, as his condition will not improve. He knew I came to see him, and we spent a lot of time together in the two weeks I was there. If he could, he would thank everyone who’s sent him good wishes and prayers.

Today’s topic came in about a week ago, and I put it in my bank of reports to write while I’m on the road. Although today is Monday, I’m still traveling home from seeing Mac. The distance was so great that I broke it into a 3-day trip, and was planning to stop by the American Pickers store in Nashville. I got there before they opened, and hundreds of people were already waiting in line to see it. So, I decided to just continue driving home.

The question is: How did shooters of old test their trajectories? How did they know where to aim for the longer shots?

I suppose the answer breaks down in several ways. Buffalo hunters, for instance, shot just one load in their rifles so that one load was all they had to learn. The land over which they shot was mostly flat and dusty so they could see the strike of the bullets when they hit the ground. Over time, they learned where to set their sights to hit animals at different ranges, and they used the feedback they saw downrange to refine their understanding of the ballistics of their rifles.

Then, there’s the scientific approach, which is based on mathematics. Calculations can be made to predict the flight of the bullet with good precision, then they’re verified and refined by empirical testing on the range. One of the best-documented instances of this is the development of the cartridge that became the .45 Government, or what we know today as the .45-70. That cartridge started out as a .50-caliber round; but through range studies and exhaustive testing they discovered that the .45-caliber bullet had better ballistics. If you’re interested in this sort of thing, there’s a very thorough report of the entire cartridge development in M.D. (Bud) Waite and B.D. Ernst’s book, The Trapdoor Springfield.

Though the timeframe for this development was the late 1860s and early 1870s, scientists knew a lot about how projectiles flew ballistically — and they had good mathematical tables to help them with their research. Ballistics was already an established field of study when this cartridge was developed.

But what about the amateurs? What did they do? Some were able to use the same tables as the scientists, and they used their own ranges to confirm and tweak the results of the calculations. But they didn’t have Chairgun back in the 19th century, so whatever did they do?

What’s Chairgun?
Chairgun, and now Chairgun Pro, is an airgun and rimfire ballistics software that helps you plot the trajectory of a pellet before you shoot. It has become a great favorite of airgunners who use it to set their scopes for different ranges with different pellets. Field target competitors find it especially useful because they need to know the exact place in the trajectory their pellets will be at all ranges. Those pellets must pass through small holes in the front of the steel targets they shoot at in order to hit the triggers in the back of the targets and knock them down. If their pellet partially hits the face of the target as it passes through the hole, it can lock the target in the upright position and it won’t fall — robbing the shooter of a point. But the Chairgun software and lots of testing helps the shooter refine his pellet plot so he gets it in the right place every time.

And the good news is that now they have a version that works on Mac computers, too, so I’ll finally be able to use it!

But 150 years ago, there were far fewer personal computers — so what did those people do to determine the actual trajectories of their bullets? Well, to paraphrase the movie, The Graduate, I have two words for you — tissue paper. They lined up tissue paper screens between the muzzle and the target, and shot through them to “watch” the drop of the bullet over distance.

Now, before some wiseacre scientist in the crowd pulls the Heisenberg principle card on me, I’m aware that passing through even one sheet of tissue paper does have an effect on the ballistic flight of the bullet, however slight. I’m also aware that a bullet isn’t a subatomic particle, but I wanted to get that idea off the table so we could discuss the thing that “they” really did in order to measure the flight of bullets.

When Dr. Mann did the 37 years of work that eventually lead to his book The Bullet’s Flight, from Powder to Target, he used tissue paper screens at regular intervals between the rifle and target. He wasn’t looking for the trajectory as much as he wanted to know the attitude of the bullet at various distances from the muzzle. In his day, it was suspected that bullets left the bore unstabilized and then stabilized as they went downrange. So, he was looking for the pattern of elongated holes on the screens that would indicate yawing bullets.

How did they align the screens?
If you have ever given this approach any thought, you must have wondered how the screens were aligned. For example, if all the screens are supposed to be the same height above the ground from the muzzle to the target — how is that done? You don’t just set them on the ground and hope they line up; because no matter how flat the ground may be, there are still variations of several inches at various points along the bullet’s path. But these people wanted those tissue paper screens to be aligned within the tightest variation possible.

Today, we’d use a laser and place the screens so each one aligned with the laser’s dot; but just as computers were in short supply back then, so were lasers. So how did they do it?

They used a surveyor’s transit to align each screen. Because of the nature of what they were doing, they had to start placing screens at the target and work backwards to the gun because each screen obscured everything that was beyond it. With a laser, you work the same way. The only difference is that one person can lay out a range like this with a laser, while a transit takes at least two people. If you’ve never tried it, don’t make light of it, because you cannot imagine the difficulty of aligning all those screens. And, if the wind is blowing, you might as well give up because the screens will never settle down.

Did it work?
Some of you know this works because you’ve tried it yourselves. Yes, it does work. The tissue paper needs to be stretched tight on the screens so it doesn’t tear. That isn’t as important for firearm bullets as for airgun pellets, but the paper does need to be fairly flat for every bullet or pellet. And airgunners usually don’t need to place screens out beyond 50 yards or so, while in the past firearms shooters often placed them out several hundred yards.

For an airgun, an interval of 5 yards is useful. For firearms going out to long distances, a 25-yard spacing might work better, though closer to the gun so that spacing might be reduced to 10 yards.

A modern anecdote
In the early 1990s, several government physicists wrote papers that criticised the story of Billy Dixon, the buffalo hunter who shot an indian off his horse at 1,538 yards during the second battle of Adobe Walls, Texas. It took him 11 shots to find the range. The physicists said it wasn’t possible for a .50-caliber bullet weighing over 600 grains and leaving the muzzle at 1,250 f.p.s. to even go that far, let alone to hit a target way out there. So, several shooters convened at Fort Huachuca, Arizona, where the U.S. Army had a millimeter wave radar to track their bullets in flight.

What they learned astounded them. A bullet from Dixon’s rifle could go over 2,500 yards, and the Army’s .45 Government bullet went past 3,000 yards. Even though they were subsonic much of the way, these bullets were proven to have very great range. This experiment could not have been done with tissue paper, since the barrels had to be elevated 30 degrees to the horizon.

I hope this answers the question our reader asked about how trajectories were verified in the past.

43 thoughts on “Testing trajectories in the past”

  1. I guess the thing that always makes me wonder about when people talk about trajectory is.I guess I will use this as an example.Look at a Major league baseball pitcher.He can throw knuckle balls,sliders,curve balls and such.Each one of those has a trajectory.Take a curve ball (it kind of simulates a pellets trajectory) and watch its flight path.It will curve to the right or left depending on the arm the pitcher throws with and it will drop as it gets closer to its point of impact because of gravity.Depending on how fast or slow he throws it will change the arc of the ball.The only good thing about what the pitcher does compared to what we do is his target is always at the same distance.When you start increasing the range or start shooting uphill or down hill things start changing(anybody that shoots knows that if you shoot up lets say in a tree or down in a valley at the same range you have to aim low for the up and down shot and how much again depends on velocity and weight).But when you talk about in the old Buffalo days they were most likely shooting to survive.I bet they did some practicing when they got a chance-And as far as that goes when I was a kid learning to shoot.I would shoot and observe.And yes you pick up pretty quickly of where the point of impact is.I would bet that is the way it was done back then. And even now days you make a cheat sheet in your flip up lens covers and the new scopes with side-wheel parallax work as good range finders.So as it goes if you can estimate(notice I said estimate your range)and practice and document or remember were to hold the sites at that range you will eventually become successful. And to me point of impact is what I look at more than trajectory.One of the old sayings go is You probably don’t want to show up at a gun fight with a man that owns one gun.Why? He knows how to shoot it.

    • Recall though, baseballs don’t just have a longitudinal spin… Heck, a true “knuckle ball” is one that is thrown with practically NO spin in ANY axis.

      Your better comparison would be to AirSoft guns with adjustable “hop-up” — which controls how much backspin the ball achieves. AirSoft don’t have rifling, so not longitudinal spin for stabilization. “Hop-up” backspin relies upon Bernoulli effects to “lift” the ball above the path gravity alone would produce (too much “Hop-up” can actually result in a ball /rising/ during part of the trajectory).

  2. Wait just a damn minute, are you saying government scientists got it wrong? I suppose next you’ll be telling me that climatologists are wrong about global warming, or that the Affordable Care Act will actually increase the cost of my health care! You sir, are treading on thin ice.

    • But wait. What about the next part? Didn’t the physicist figure out why they were so far off? Basic to the scientific method. I would be really curious. It’s not just government physicists. My cousin is a brilliant retired professor of physics. Any science problem that I have ever alluded to here would be complete child’s play for him. But he’s not familiar with shooting and when talking about the range of pellets, he did a calculation and said that he really could not see how an airgun pellet could travel more than 100 yards. Believe me, his intelligence and knowledge of physics is not in question. You won’t find better. But if it’s not that then it’s…. I can only conclude that our science, for all its achievements is just scratching the surface of what’s out there. I’ve heard a story that French engineers, real Inspector Clouseau types, proved beyond a shadow of a doubt that bumblebee cannot fly.

      What was the Indian doing on his horse while the shooter was ranging shots at him?


      • Matt,

        The tribal medicine man had supposedly painted all the men and horses with paint that made them invisible to their enemy. Dixon fired 11 shots before connecting, and I think the brave who was shot was standing still on a dare.


  3. What does Mac have?——— And what bothers me is that there has been a bunch of knowledgeable people in my life that I got the honor to know.And when this time comes I only hope that the knowledge got transferred on that he was able to give.There are certain people through out life that you just know you have to listen to.There was a man that was a little older than my Dad that he was friends with for along time from when they were kids.He owned a hobby shop.He is the one that taught me about building planes,making the motors faster and so on and muscle cars(he had a 69 Z28 Indy Pace Car with the 302 Zapper and 4spd. in it) .He was always like a kid at heart.Was like 83 years old and still went to his little hobby shop every day.Always fun to talk to and never left the place without learning something new.My Dad made guitars as a hobby.And I learned alot from him.All I know is the words that should be spoken are always to late. Praying for Mac

  4. Wow,50 something years old(I think)and again after reading my last reply I’m in trouble again.If my Mom read this she would almost whop me up side my head.Yes Mom I learned alot from you too.:)

  5. B.B. and Edith,

    On the subject of trajectories, I found myself wondering this morning what the trajectory might appear to be for the landing of the Condor SS (unveiled months ago and one the Pyramyd AIR site for weeks now) and the Benjamin assisted handpump (a conspicuous absence). The Condor is estimated to arrive at P.A. in two days (4/24/13). Any chance of that happening? If not, any idea of what the new delivery estimate will be?

    As for the Benjamin Assist pump, might the naysayers be right, that this is a fake product like the Crosman TX200 clone?

    I ask because several months ago I decided to make a pre-emptive entry into the Dark Side, but I haven’t touched my Marauder and Hill pump in about two months. They have literally collected dust, and I am strongly considering leaving the Dark Side for good. It was the promise of MUCH better things to come that got me to take the plunge, but for some time now, all I’m feeling is wet.


    • Michael,

      The Condor SS rifles are shipping right now, so Pyramyd AIR should get theirs soon. As for the Benjamin pump assist, I think I mentioned that Crosman expects it by early summer. If not that’s what in was told.

      The problem is, you are looking at data from a wholesale show, and the delivery dates can be up to 12 months from then. As for the naysayers, I generally disregard them, as they seldom get it right.


      • I must have missed the comment about the assisted pump expected in the early summer. I miss a lot of things, although usually they’re tiny little dots on paper ten meters away!

        The news about the Condor SS is exciting.

        Thanks much as always,


  6. B.B.

    I was afraid you were going to say something along those lines about Mac’s situation. Wish it did not have to be so. Good people and friends are too hard to find.


  7. BB,
    I just jumped on quick hoping to see an update on Mac. Thanks for the update, even though it is a sad one. I have lost two guys that were my best friends at the time to cancer. It is tough and I still miss them. As you said though, there is a better place where there is no suffering. Have a safe trip home,

    David Enoch

  8. My gym class used to carry out trajectory experiments on a weekly basis. This was in the 70’s before the PC crowed outlawed our experiments. We called it dodge-ball.We carried out our experiments so well that we could zing the lurkers at the back of the gym with one quick glance and a fake to a team mate.While there were no buffalo guns and Indians, it was till a hoot, and a learning curve. The best trajectory i ever witnessed was a fellow who threw so straight that the ball actually hit himself in the back of the head. What happened is he slipped while throwing, the ball went straight up,he hit the ground and the ball came directly down on himself. HE Shot himself out of the game of dodge-ball !! Now that the PC crowed has outlawed this fine experiment in trajectory our “new scientists” are stuck with virtual dodge-ball. So much lost.

  9. I’m sorry to read that Mac’s time is almost up, but I’ll keep him in my prayers. The older we get, the more friends we lose this way.

    I’ve been out to Adobe Walls. I used to live in the same county, Billy Dixon was the first county Sheriff.
    The whole area is much the same as it was then. The road it is located on doesn’t really go anywhere else, so few people venture out there. The ruins of the old buffalo hunters’ fort are still visible. The plum thicket by the Canadian River where the Indians picked plums is still there.

    You can stand at the ruins and look to the bluff where the Comanche was killed. It is a great distance, but consider Dixon himself was a buffalo hunter, and used to making long-range shots.

    While I was there, I met a very old man who told me he had grown up on the Comanche Reservation in Oklahoma. The battle was an important part of their oral history. He told me this gem that didn’t make it into the history books.

    The buffalo hunters had a large, Rottweiler-like dog with them. The dog was fighting the Comanches, too, running out of the fort to attack them. The Comanches killed the dog (that much has been documented in books).

    Here is what wasn’t published. The Indians scalped the dog, and took the scalp back to camp with them. They left the ears attached.

    The kids there had fun wearing the dog’s scalp as a cap, the ears flopping around sort of like a Mickey Mouse hat. I can imagine them re-enacting the battle, one kid playing the part of the dog.

    Even the old man would have been too young to have witnessed that. But he knew the story well, and might even have seen the dog’s scalp.

    Billy Dixon had some good company at Adobe Walls. Bat Masterson was one of the other buffalo hunters there. There were more, too. I think they were working out of Dodge City, KS.


  10. My sympathies and prayers for Mac. Glad that B.B. was able to spend time with him. Keep us informed.

    What’s the American Picker store?

    That’s some painstaking stuff with the tissue paper. I bet Frank Mann was right in there with the best of them. This may have been part of a whole weird class of experiments that no longer take place. The word is that in tests of the British Enfield rifle, they would take picked marksmen and do volley firing at a sheet of cloth the size of a house that was placed 3000 yards away. What was that supposed to prove? I guess you could see why they were using such high power cartridges in the battle rifles.

    By the way, what’s the story on the .45-70 government cartridge. I know it’s historical. Was it any good?

    The Graduate is my favorite movie of all time. The quotable lines are endless.

    Father: Ben, this sounds pretty half-baked.
    Ben: No, it’s completely baked.

    But for my money, one of the best quotes appears in the book version but not the movie. Benjamin, the scholarship student, writes a break-up letter to Mrs. Robinson that ends. “I want you to know that I have thoroughly enjoyed myself and I feel, as I hope you do, that this has been a valuable part of my general education.”


    • While the Trap Door Springfield Rifle 1873 was so so, the .45-70 cartridge was and is a winner. It’s still in common use today. I use it in an original 1873 for Cowboy Action Long Range. The 300 yard buffalo is no problem!


    • Matt,

      The American Pickers TV show has a store in Nashville where they sell the stuff they pick. It’s called Antique Archaeology.

      The 45-70 is a timeless classic round.

      Shooting at a target the size of a house was to demonstrate the effectiveness of plunging fire. In WWI the tactics were to elevate all the rifles and fire so their shots would converge on the enemy positions from a high angle — plunging fire.


    • I have a friend who loves participating in cowboy action shooting events. He is a Vietnam Vet and a licensed gun dealer. He was even my foreman a long time ago. We used to have a few beers and talk for hours about all kinds of things and a lot about weapons. From what I remember, the .45-70 was usually described as being pretty deadly and had some range. Unfortunately, the trajectory was more like water out a garden hose when compared to more improved ammo.

  11. I suspect that many interesting empirical experiments have been replaced by computer models. This has to be much less fun for the experimenters.

    Plunging fire vs. direct fire has been of special interest in the field of naval artillery. This is because of the need to devise armor types to defeat the shells, and shell designs to defeat the armor. It also led to the theory of “zones of immunity” for armored ships. A zone of immunity is a set of distances, minimum and maximum. The minimum distance, at which the zone begins, is the distance where direct fire is ineffective against side armor. This side armor consisted of heavy belt armor, backed and augmented by internal armor that was sloped. The idea was to cause the cap to come off the shell. and to cause the shell to detonate and deflect before penetrating the innards of the ship. Additional layers of lighter armor were designed to stop shell fragments.

    The outer limit of the zone of immunity was the range where the ship would be vulnerable to plunging fire. Plunging fire became more effective as distance increase, as the heavy shells would be impacting from a greater height. The zone of immunity was that distance between far enough that direct fire was ineffective, yet close enough that plunging fire was ineffective.

    The first use of fire control computers was on warships. These computers were huge, electromechanical devices that factored in not only range, but speed and course of target, and the effect of roll of the ship.


  12. Again,so sorry about Mac.I know for certain many prayers came his way.It is really too bad you weren’t
    able to hook up with Antique Archaeology! You could have been on their speed dial to keep them from spending many hundreds of dollars on completely unsavable BSA’s!

  13. While going through some old magazines, I found a copy of “Airgun News & Report”. It’s Vol. 1, No. 1, the premier issue circa 12-1985. Things sure have changed!


  14. Well a strange gun control has just hit my range today. I had a going argument with Frank. It’s his property i hunt pests on. Incidentally that is also where I keep my arsenal of guns. He was adamnent I must use one of his shotguns to hunt with this year. I do not like shotguns so I pulled out my AK47 for the purpose. After 40 shots zeroing in that gun he changed his mind and said he’d rather I use my custom Condor with it’s custom shrouded 24″ barrel to hunt pests with. Apparently the noise of some simple target practice and sighting in of the gun got to him. It’s not a gun issue it’s a noise issue. So in the end I got what I wanted which was to hunt with my condor anyway. I guess that AK47 had it’s uses in my hunting arsenal. So this year my battle plan is to trap the groundhogs since I have good success with that, use my condor for muskrat and when I get one that just refuses to die I get to take a shot with the AK47. But the condor must be the first gun i use. So I’m a happy gut today. I got a lot of money into that condor and it’s the most accurate gun I own. My Discovery is second best. I had that one out today too. Once I had the scope zeroed in I could hit what I chose to hit. (it’s also heavily modified.)

  15. But 150 years ago, there were far fewer personal computers — so what did those people do to determine the actual trajectories of their bullets? Well, to paraphrase the movie, The Graduate, I have two words for you — tissue paper. They lined up tissue paper screens between the muzzle and the target, and shot through them to “watch” the drop of the bullet over distance.

    Now, before some wiseacre scientist in the crowd pulls the Heisenberg principle card on me, I’m aware that passing through even one sheet of tissue paper does have an effect on the ballistic flight of the bullet, however slight. I’m also aware that a bullet isn’t a subatomic particle, but I wanted to get that idea off the table so we could discuss the thing that “they” really did in order to measure the flight of bullets.


    You’ve just described my “independent” experiment for high school physics — in which I set up a line of cardbard frames holding onion-skin paper in the basement and used some BB gun to fire the length.

    Not the best experiment as I had very erratic frame positions…

    • That reminds me of a You-tube video that came out around Easter time. How many marshmallow Peeps can a .50 cal. bullet go through?

      Less than you would think. In the video, about ten feet or so of Peeps were lined up on a plank, and a single .50 cal. rifle shot fired into the first Peep. After about three feet of marshmallow destruction, the bullet was deflected enough to veer off to the left, leaving the rest untouched.

      I found this quite unexpected, until I remembered the Myth Busters firing a .50 cal. into water. It only took three feet of water to expend all the energy in the round.

      My previous experience with Peeps was on a railroad. We would put them in a microwave. They would blow up enormously, then collapse like a deflated balloon. We found that quite amusing.


      • They would blow up enormously, then collapse like a deflated balloon. We found that quite amusing.

        That sounds like footage I saw at a small gun store in the late seventies… One of the .17 caliber centerfire rounds, target subject: prairie dogs…

        They, too, puffed up into a near spherical shape, then collapsed into a small mound…

        Morbidly amusing…

  16. BB,Thank You.That answers the question and was great fun to read too.Not just the military,but maybe even NASA benefited as the knowledge and understanding continued to progress right on to the space age.Gee,I wonder what the ballistic coefficient of a space capsule is?Now wouldn’t that shape make an interesting pellet?

    In regards to Mac;the number of his days was written before even one came to pass.We don’t know that number so we should continue to pray and also for his comfort.-Tin Can Man-

  17. I guess I’m lucky where I live.In my back yard the terrain is like this.Center and to the right the ground is flat then about 40yrds.out the woods start and go uphill at about 40 degrees to the top of the hill to about 75yrds. Straight out the ground is open and flat for about 150yrds. Then to the left it is a slow 15 degree down hill to a creek that is about 75yrds.out.So I have a very good variety of a shooting range.Probably the up hill part of the ground is the best for naturally testing trajectory when the leaves are on the trees and brush.I will place targets at different ranges on the hill.And guess what.The leaves act like the paper or tissue being placed at different spots to the target.Not all the time but pretty well most of the time I shoot at the target and can watch the pellet make holes in the leaves that was maybe a inch and a half to the right of the target and maybe lets say a inch high depending on the range.And hit dead on bullseye to the target I aimed at.As far as the straight and level and down hill part of the ground is concerned it is great for getting range point of aim figured out on the hold over or under.And sometimes I cant wait for a windy day to to check the point of aim on windage.I remember when I was a kid I didn’t like shooting on windy days(as it goes my dad would say that was the days you should be shooting on.You will be surprised what you learn).He was right again.

  18. Sorry to hear about Mac.
    Do you have a reference for the army millimeter wave testing involving firearms. I always hear 45 deg for maximum range. With air resistance it’s 32 degrees. From what I understand the army tested 45 acp and other cartridges.
    Web search only say it been done, but they never give an actual report or publication.
    I’d appreciate any help you can offer.
    Thank you

  19. Trajectory, Range and Windage oh my. Using a multiple target sheet, my testing starts at about 10 paces/yards shoot five, move back 10 shoot 5 and repeat until I can’t hit the target very well. Then then study the results.

  20. For some reason the movie Dances with Wolfs keeps running through my mind,When the Buffalo herd finally came and the Indians and Lt.Dunbar are looking over the top of the hill down onto the range.Lt.Dunbar is looking through his spotting scope and he shows it to the Indians and you see their eyes light up.Then when it comes time for the hunt and they are chasing the Buffalo it gets pretty dusty.Then at some point of the hunt Lt.Dunbar flips up his sight on his rifle to take a shot at the charging Buffalo to save the young Indians life.I think I remember him taking something like 3 shots before he hit the Buffalo and it stopped at the Indians feet.I wonder if he was missing because of the rushed shot he had to take to save the Indian.Or if he was using the dust in the air and/or the bullet impacts to range his shots.I know it was a movie and an amazing shot at that for the fact that he was shooting from a moving horse.But I just bet the dust helped in some way.And I wonder if while he was in the military before he went into the great frontier to become Dances with Wolf.If he got to look through his spotting scope at the shots of the soldiers he was probably training.I know that I have seen bullet and pellet flight paths through my spotting scope and rifle scopes.And on another aspect my Dad was a Civil Engineer in the Korean War and their job was to secure,survey and keep the the Soldiers and Doctors,Nurses and so on safe.They always ended up having unwanted visitors at the most inappropriate times.Mostly at night.He didn’t have the luxury of a night vision scope and he couldn’t see his impact in the dark.They had to listen for where the shots came from,shoot and listen for his impact.He said he would make sound diverters(not suppressors)so it would send his shot report in a different direction.That way if the enemy returned fire they probably shot in the wrong direction.

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