Optimal angle

Short answer - Chairgun/Strelok tell you the truth.

Short-ish answer - for firearm/airgun the max range angle is generally somewhere between 25 and 35 degrees depending on the BC. 

Long-ish answer: If we lived and shot in vacuum, say on the moon - the optimal angle would always be 45 degrees. Alas, not too many squirrels live there, so here we are ...
As soon as you add atmosphere - your good question has no single answer, because it depends on the air resistance, which itself depends on atmospheric pressure and the projectile BC. I can elaborate on physics, which is quite simple in this case, if this if you find it interesting.

A bit of curious history: One counter-intuitive example of a super long range artillery is the K-12 railway gun, it was shot at nearly 60 degrees. What the heck, you might rightfully wonder ... Well, the answer is that by shooting up, the projectile would clear much of the atmosphere before reaching the apex of its trajectory, and traveling with far less drag, even for part of its trajectory, even at such sub-optimal angle, was more effective as far as range goes than shooting at sub 45 angles used by regular guns. Don't try it at home with your PCP, you'd need to get the pellet to stratosphere for this work, in which case aiming and calculating holdover might become hard. Even fx "no limit" rings have a limit :)

 
Here is your answer. So far as I know my research was the first attempt at establishing a result for air rifle diabolo pellets.
Greg may find this of interest.

Back in 2004 on another forum I asked the gurus and pundits the question as I was concerned about city shooters missing a bird and lobbing a pellet in somebody's house some blocks away or worse. The guesses were guessed but one Steve Woodward came up with a plausible answer. I then had a little competition for folks to design a portable way of determining elevation angle for me to easily carry and set up at our farm wherever I wished. Again Steve made a suggestion; here it is, The original DangleOmeter which uses a gravity weight and geometry set for any given angle and raised until the strings are tight to determine when the elevated rifle is correct for that angle. It all fits into a 35 mm film cassette:

DangleOmeter geometry:

After preliminary tests at 6 degrees elevation showing pellets lobbing in a dam near the far bank at measured 500 yards, I tested Steve's maths.
My average of 712 yards at 25 degrees (see referenced thred below for details) and Steve's prediction chart, for the particular pellet and rifle's external ballistics, was very coincident giving credibility to the chart:

Actual Terminal ranges.
MV-fps 500 550 600 650 700 750 800 850 900 950 1000
- BC -------- Terminal Range-yards ---------------
0.0050 115 120 125 129 133 137 140 144 147 150 153
0.0075 155 163 170 177 183 189 194 199 204 208 212
0.0100 191 202 211 220 228 236 243 249 256 262 267
0.0125 224 237 249 260 270 279 288 296 304 312 319
0.0150 253 269 283 296 309 320 331 341 350 359 368
0.0175 281 299 316 331 345 359 371 383 394 404 414
0.0200 306 327 346 364 380 395 409 423 435 447 458
0.0225 330 353 375 395 413 430 446 461 475 488 501
0.0250 352 378 402 424 444 463 481 498 513 528 542
0.0275 373 401 428 452 474 495 515 533 550 567 582
0.0300 392 423 452 479 503 526 547 567 586 604 621
0.0325 410 444 476 504 531 555 578 600 621 640 658
0.0350 428 464 498 529 557 584 609 632 654 675 695
0.0375 444 483 519 552 583 611 638 663 686 709 730
0.0400 459 501 540 575 607 638 666 693 718 742 764

And one showing the optimal angles:


"Yrrah - Here's a more complete "Optimum-Angle VS MV" Terminal Range tableJanuary 2 2004, 10:56 AM Note that it does suggest raising the DangleOmeter setting a bit for 600fps.

MV-fps 200-300--400-500-600-700--800-900-1000
- BC -------- Optimum Angle (Degrees) ---------------
0.0050 30.2 25.7 22.7 20.4 18.6 17.2 16.1 15.1 14.2
0.0075 32.4 28.0 24.8 22.5 20.6 19.1 17.9 16.8 15.9
0.0100 33.9 29.6 26.4 24.0 22.1 20.5 19.2 18.1 17.1
0.0125 35.0 30.8 27.6 25.2 23.2 21.6 20.3 19.1 18.2
0.0150 35.9 31.8 28.6 26.2 24.2 22.6 21.2 20.0 19.0
0.0175 36.7 32.6 29.5 27.0 25.0 23.4 22.0 20.8 19.7
0.0200 37.3 33.3 30.2 27.7 25.7 24.1 22.7 21.5 20.4
0.0225 37.8 33.9 30.8 28.4 26.4 24.7 23.3 22.1 21.0
0.0250 38.3 34.5 31.4 29.0 27.0 25.3 23.8 22.6 21.5
0.0275 38.7 34.9 31.9 29.5 27.5 25.8 24.4 23.1 22.0
0.0300 39.0 35.4 32.4 30.0 28.0 26.3 24.8 23.6 22.5

0.0325 39.3 35.8 32.8 30.4 28.4 26.7 25.3 24.0 22.9

0.0350 39.6 36.1 33.2 30.8 28.8 27.1 25.7 24.4 23.3
0.0375 39.9 36.4 33.6 31.2 29.2 27.5 26.0 24.8 23.6
0.0400 40.1 36.7 33.9 31.5 29.6 27.9 26.4 25.1 24.0
0.0425 40.3 37.0 34.2 31.9 29.9 28.2 26.7 25.4 24.3
0.0450 40.5 37.3 34.5 32.2 30.2 28.5 27.0 25.7 24.6
0.0475 40.7 37.5 34.8 32.5 30.5 28.8 27.3 26.0 24.9
0.0500 40.9 37.8 35.0 32.7 30.8 29.1 27.6 26.3 25.2

End quote.
Now I know some would be interested in the project so here is some reading circa 2004. Unfortunately the pictures of the test scenery were in Hunt 101 which went defunct , I will try to find them in my file and re-post them:

http://www.network54.com/Forum/79537/thread/1079572300/%3C/a
Note the rifle used was not the Benjamin 342 shown in the pic above.

Subsequently Dave Eade used this as the basis for the maximal range facility in Chairgun.
Note: in a vacuum 45 degrees would be the optimum for all scenarios. We are discussing barrel projection angle here, not line-of-sight as Azuaro may have implied above.

This is probably more reading than you bargained for but there was a lot more in the background and follow up than is presented above.
For example, the question of terrain came up when a few yards difference was noted between Steve's prediction and my result. This lead to my establishing that the shots were in fact down hill at approx 1 degree. the 6 degree 500 yards shots were in fact at 7 degrees and when that was factored in the coincidence was incredibly close. Apogee of trajectory and air density changes were also discussed:
http://www.network54.com/Forum/79537/thread/1079996983

Please enjoy the read and comments are welcomed. This logistics of this stuff took much more time than writing up a simple report, or taking a wild guess based on limited heresay. ... Best regards, Harry in OZ.

 
Paulcat - thank you. But I can't take credit on Aussie behalf for the DangleOmeter. I posed the question for a very portable instrument and Steve Woodward from North Carolina USA invented it for me. Steve has electronic gadgetry in the Mars Probe but loves a challenge that resolves concepts, ideas AND details, distilled to the bare essentials. I have other digital angle measuring devices, but none so portable and yet also accurate. The different angles are set by drawing one Kevlar thread through the lead weight,

AZ I don't know how you got 609 yd at 23 degrees from Chairgun for your 10.34 gr JSB at 925 fps ... but my check on your pellet at that MV shows Chairgun to need a BC input of a whopping 0.0351 NTP or 0 .0387 at your elevation at your stated 54 d F to get 608 yards at 28 degrees elevation! ... I'd sure love to have some of those .177 JSB Heavies in my shooting box as it is close to the BC of .25 cal JSB 25.4 gr Kings!


A more realistic set of data would use a BC of NTP 0.0245 or 0.027 at your altitude, which I have established as 2,894 ft, plus the 10 ft to your bench. ( Note the Chairgun database showing 0.031 is a misprint as that is the BC for the 15.9 gr JSB .22 cal Exact).

Here is what it then looks like (correct for your altitude):

You might note that the range given at 40 degrees matches your figure precisely, which I expect is a real coincidence.

Not sure what your observer was doing with the binoculars; neither of you was up where the action was. You were using a spotting scope which you presumably used to spot shot fall, then swapped it for the laser rangefinder to measure a now guessed location on the water at an approximate 1.30 degree angle to the water at 400 yd or 2.09 degrees at 250 yards. Lasering on glassy water at that shallow angle and discriminating to 0.79 of a degree I assume would be a guess at best.
I think you may have wrapped this one up with these quotes, "...hit the water at around" ... and, "...it was about the same but we couldn't precisely tell...I wish I could've used a spotter near where the pellets were landing for better accuracy at these distances".

That is precisely why my wife (shielded) recorded the PsOI while located beside the small dam and close to the shot fall .

Other than reading about it I don't know what your experience in respect of mortar fire may be, its ballistics and importantly its purpose. My own understandings come from being a trained bombardier in an artillery unit using mortars and field guns. 
It isn't AG related so I don't intend working through that here now as it involves trigonometry and calculus which I'm sure you wish to be spared. 
Perhaps don't sell our readers short though with this sort of advice ... "But don't get involved in the formulas and modeling because you will be overwhelmed...Read and understand CONCEPTS and IDEAS....Intelligent people discuss concepts and ideas and not details..."

My observation is that many readers here are intelligent, can feel at home with ideas and concepts; and actually seek to work through the details that may reward them with finer shooting. ... Regards to them all , Harry.


 
I love these types of discussions! Harry, here is one to ponder when you're lying awake wondering why you can't sleep!

One of the known, but apparently ignored factors of naval bombardment doing WWII, was the critical barrel elevation angle, with respect to the projectile's longitudinal orientation at the POI. As we know, naval guns, rifles really, have a maximum angle of elevation of ±35°. As a result, the shells, all 2,200 pounds of them, just landed on their sides. Other than the crater caused by their detonation, the shells did not penetrate the surface. Howitzers on the other hand, can be elevated past the critical angle, ≈47°, so the shells land essentially point first, and easily penetrate the surface quite a distance before exploding. Sort of a bunker buster as it were.

The reason I bring this up is... I wonder if diablo pellets exhibit the same phenomena? 
 
Yrrah or Harry or whatever:
We have innumerable landmarks along the shoreline and this is a pristine lake (Turquoise color)...I don't believe that you have any foundations nor support for your discrediting comments. Rephrase...You sound arrogant, respect other people's ideas and speak about your own findings and understand that neither you nor I are not above no one...After all, you don't know who is at the other end of the line.

AZ 
 
"Alan"I love these types of discussions! Harry, here is one to ponder when you're lying awake wondering why you can't sleep!

One of the known, but apparently ignored factors of naval bombardment doing WWII, was the critical barrel elevation angle, with respect to the projectile's longitudinal orientation at the POI. As we know, naval guns, rifles really, have a maximum angle of elevation of ±35°. As a result, the shells, all 2,200 pounds of them, just landed on their sides. Other than the crater caused by their detonation, the shells did not penetrate the surface. Howitzers on the other hand, can be elevated past the critical angle, ≈47°, so the shells land essentially point first, and easily penetrate the surface quite a distance before exploding. Sort of a bunker buster as it were.

The reason I bring this up is... I wonder if diablo pellets exhibit the same phenomena? 


Alan: " I wonder if diablo pellets exhibit the same phenomena?"
To a point some do and others don't. The latter are the ones which are most useful at the longer ranges.

None of the pellets actually land on their rear end (drag stability helps) but can impact with considerable yaw. Those which may lose dynamic stability, generally it seems through loss of tractability beyond their critical upper register angle, undergo increased yawing/ precession that results in spiral flight. Accuracy degrades at that point.

By way of illustration, here is a video I made that shows tractable flight with the pellets' axis following the trajectory curve (Stratons): and a contrasting clip showing pellets (Gamo Masterpoint) which lose ability to maintain their axis aligned with trajectory as they pass the curve apogee and so lose dynamic stability and begin to spiral;
http://vidmg.photobucket.com/albums/v392/Kyogle/StratonGamoMasterPointflightcomparison.mp4
The Stratons demonstrate the perfect flight and resulting accuracy, The Gamo shows an inability to do so after it passes the flight apogee.
The smooth bore mortars projectiles were fin stabilized as an arrow and so landed point first regardless of elevation. With no spin they cannot be over stabilized. Our 25 pounder field gun/howitzers did a pretty good job of making large craters even 8 miles out!

Hope I have somewhat answered your query Alan, and I'm hoping the video shows. ... Best regards, Harry.

 
"
There are days when there is no sun reflection on the water, no wind and the lake/water is like a mirror with lots of light…" .... "Today was one of those good days for testing..."
AZ you implied that the water was "like a mirror" - to me that's "glassy". OK?

It was you who introduced reference to artillery ballistics , not me. I simply indicated my artillery experience base; and implied that I thought mortar ordinance was not particularly relevant here.

You were purporting to critically analyze external ballistic material, such as that in Chairgun, and then write , " We had communications as simple as "It landed before the white boathouse by the Serbian Spruce that is about 100 ft. back of the big rock" ...
Then you try to accurately measure to a dissipated splash 400 yards away on a mirror surface at a 2 degree angle incidence of viewing. I again say it is a guessed result regardless of the measuring instrument's quality.
An instrument is only as good as the criterion method of use. Sloppy method = garbage data. Your engineering background should endorse that observation. The results in no way make a valid case for dismissing Chairgun's actual estimates.

So, about that 609 yards from Chairgun "data" you continue to quote: It was not 609 yards because no one including Chairgun said it would be.
I took some time to present a Chairgun chart that indicated you perhaps used a very unrealistic pellet BC to derive that figure; and you implied Chairgun to be way off base. 
So, do you really have a 10.34 gr JSB .177 pellet with a BC as high as a .25 cal JSB 25.4 gr King: If so could you mail me a few tins at my expense for testing and reporting back to Pavel and Josef for them to identify the particular die/s for this revelation. Those pellets will be huge news on the world benchrest scene. 

In respect of "Government or private sector" decision making, there is a wise old saying that "The Devil is in the details" and that is "where the rubber meets the road". So, perhaps at least give the nod to accurate "details" already established. However much of what there is to know about our game is possibly yet to be researched. With the employment of sound methodology you may be able to contribute as you seem to have the facility and the time.

Introducing complex concepts, then attempting to oversimplify their exploration is a sure way to promote and perpetuate misconceptions (like 45 d is the optimal angle for projectiles to achieve their maximum range - it is not); and referencing historical data to support such oversimplifications often compounds the confusion as readers struggle to reconcile the misconceptions with the detailed, often valid, historical findings. You may recognize other examples here.

On the personal note you introduced, you wrote, "I (you) don't read your posts nor participate in your threads because of the too technical too complicated approach ... " - Then how is it, that without reading my input here, you seem to be able to quote me so freely? 

The good questions asked here and variety of subject matter presented, are testament to the interest and intelligence of our readers. They will determine what they take from it all. No one needs to apply some arbitrary boundary to contain their thinking. This forum may be big enough to support everyone's degree of interest. It has made a good start. 

I shall stop my input to this thread now excepting as I may be asked direct relevant questions.
I am sorry you consider my input as hijacking the thread rather than as critical discussion.
Wait! it was Sprocket's wasn't it?
Best regards to all, Harry.





 
"Sprocket"Wheeew! I'm sure glad I didn't ask what the optimal angle would be in zero gravity.
Take a guess... and .... you are correct ...( in a vacuum) ... Otherwise I think it's a case of, "How long is a piece of straight string", as air will stop it according to its drag coefficient/ BC somewhere along a straight line and it will just sit there ??? ........... :) ........ 
Thanks for the discussion Sprocket ... I hope you didn't think I hijacked your thread and that you got something from it all! ... Best regards, Harry.