Power Curves & the Sweet Spot

Power Curves & the Sweet Spot

Postby Mark112 » Mon May 23, 2016 6:09 pm

INTRO

I often see the question raised as to what a power curve is and what is the sweet spot. This is written as a reference to those questions and is aimed squarely at the person new to Pre changed pneumatics (PCP) in particular. I've used my S410 carbine in .22 as the example in this text.

The POWER CURVE

I'll split the firing of a full charge of air into 3 phases:-

1. When you start shooting your PCP from it's maximum fill pressure shot velocities will initially be low. This is because the hammer has to open a valve with say 190 bar trying to hold it shut. It takes a few shots before the velocity slowly climbs.

2. As you continue to shoot the cylinder pressure reduces and the valve becomes easier to open, pressure is still good and shot velocities will rise and then level out. The rifle is running at its most efficient.

3. Toward the end of the fill the valve is easy to open but as pressure is now low, at say 110 bar and downwards, velocities are now decreasing. You will now be noticing that the shots are no longer reaching the Point of Aim. This last bit happens usually fairly rapidly. You've run out of air!

If you plotted all of the velocity readings on a graph you would see that it looks like the arc of a rainbow. This is what is meant by the 'Power Curve' and most (Non-Regulated) PCPs will exhibit this trend. The following is a graph from a spreadsheet showing the curve of my .22 S410:

PowerCurve.jpg
PowerCurve.jpg (147.89 KiB) Viewed 2279 times


The velocity line is the one in pink and is slightly 'spikey' The smooth arced line is just an 'average' based on the spikey one. The other straight lines are discussed a bit further on when the 'Sweet Spot' is explored more.

Data for the graph comes from measuring every shot taken from my gun from it's full 190 bar charge down to, in this case 90 bar. I could have shot more but it was obvious at this point that velocities were rapidly falling with every shot. It's a bit of a pain to do but it will enable you to get the best from your rifle.


The SWEET SPOT

Having got the gist of the full power curve the 'sweet spot' is just the best bit of the full power curve i.e. the bit of the curve that the rifle is performing at it's most consistent. It's also in most cases the point at which the rifle is producing the most power.

As an aside if you have the capability/skill/chronograph you will need to know the cylinder pressure at the peak of the curve (in the above graph from about 130 to 120 bar) if you need to make any power adjustments. Don't set it at 190 bar to 11.8 ft.lbs as it will be over power at 130 bar!

Determining the sweet spot.

I typically use a figure of 1.5% to determine what tolerance to use for the sweet spot. What I mean is that I find the highest velocity (in the example it was 569 fps) and determine 1.5% of that. So 569 x 1.5 / 100 in other words 8.5 fps. I'll round this up to 9 for convenience. So the sweet spot is the block of shots that falls between 560 and 569 fps. In my example its the 26th shot up to the 90th. These are my best 65 shots and my particular spreadsheet shows that they have an average velocity of 565 plus or minus 4.5 fps. The graph also shows that this happens at a pressure level of between 164 and 98 bar.This is shown on my graph as the shots between the two orange lines. The red line is the average of those shots.

If I was shooting a series of long range shots and wanted even greater consistency I may choose to base my best shots on a 1% sweet spot (say 7 fps). I'll get fewer though, 48 in fact, .. you cant have everything!

Ultimately it's up to you what you determine to be the sweet spot as will have an effect on accuracy especially at longer ranges. The next section will give you an idea of what this actually means when you are shooting and you don't have to read it. I just goes a bit deeper into what this all means at the target end of things. Read at you own peril as it goes a bit deeper ...

What effect does this have when I am shooting?

To show what effect I am going to make use of a bit of software on my PC called Chairgun. It is available from Hawkes website and is a free download (certainly at the moment). It's a useful tool and with the right info input it can give some fairly accurate results. I am not going to explain how to use all of the features of Chairgun as it will take far too long as is not really what this post is about. I will however make use of the 'Vertical Stringing' feature which is found under the 'Toolbox' dropdown menu.

I've put in some figures to have a look at. and it now shows the following:-

ChairgunVS.jpg
ChairgunVS.jpg (73.27 KiB) Viewed 2279 times


Scope height you will need to measure and is centre line of barrel to centre line of scope and is 1.6 inches on my .22. Zero range is obvious really and in my this case 25 yards. Ballistic Coefficient it taken from Chairgun's tables of data and for my air Arms Diablo Fields is 0.0310

I have entered my average velocity of 565 and have put 4.5 in the 'Variation' box (remember its +/- this figure so this is my 1.5% sweet spot figure. I have picked the 'Relative to mean MV' option as I just want to show what effect 9 fps (in this example) makes.

Look at the white box on the right hand side of the last picture and look at the line say that starts with the number 25. This is my zeroed range. The second column of this line says -0.06 and the fourth column says + 0.06. This shows that some shots can be .06" (inches in my case due to my age) low ranging up to being 0.06" high. In other words using the shots in the sweet spot will lean to a variance of up to .12" (about 6mm) at 25 yards. Don't forget this is merely the inaccuracy your rifle is giving and excludes your own errors. You may be inches off!

This difference at 50 yards (read from the same chart) is minus .25 to plus .25 of an inch so the effect of the power curve just in the sweet spot will be .5" (12.5mm) at that range. You will still have to aim above the target though if you are still zeroed at 25 yards but it shows that the rifle alone could give a spread over half an inch over those shots.

Working backwards

If you know that you are prepared to accept plus or minus say .2" at 35 yards you can work back to determine just what part of the power curve to fill to. Change the figure in the 'Variation' box until it gives you .2" in columns 2 and 4 on the 35 yard line. In my case putting 7.7 in this field gives the desired result. As this is a +/- figure it means a spread of 15.4 fps in my original graph. I'll put in 15 though as I like round numbers and this would mean I could fill to 187 bar and get 94 shots within an acceptable accuracy level.

If you are shooting at say 50 yards and you need to use the absolute best part of the power curve to achieve a variance say of +/- .2" at 50 yards. Entering 3.6 in the Variance box achieves this so I'll use a total spread of 7 fps (I've rounded down 7.2) in my spreadsheet. A fill to 160 bar will give 59 shots within this somewhat narrower band.

Phew it's over

I'm done writing now and I hope this is of some use to some of you or a lot of use to a lot of you (or indeed any combination). I know some will say that it assumes that the pellet data in Chairgun is correct etc. All I can say about this is that Chairgun gives a good idea of what effect the power curve will have at point of aim and until something better comes along then Chairgun is what I shall use. There are ways of making the Chairgun data more accurate (i.e your own calculated values for BC for instance) but this is not the intent of this text. It's a fairly basic user guide to power curves and should be considered as such.

Mark

v1.0
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S410K .22 - Hawke Sport HD 3-9 x 50 AO IR
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Re: Power Curves & the Sweet Spot

Postby Roger5 » Mon May 23, 2016 7:37 pm

And now you know why a regulator can be a handy thing to fit in your rifle. Rog
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Re: Power Curves & the Sweet Spot

Postby Mark112 » Mon May 23, 2016 8:01 pm

Hi

With a spread of 15 fps yielding 94 shots with +/- less than a pellets width at 35 yards I wouldn't bother with this one (.22 carbine). I just enjoy its simplicity and reliability. It's one of my main hunters especially in wooded areas where shots are at shorter ranges. My .177 classic though I will fit a Robert Lane reg to at some point as the benefits come from consistency at the longer ranges I shoot with it.

Mark
S410C .177 Regged - MTC Viper 4-16 x 50
S410K .177 Regged - Hawke Nite-Eye 4-16 x 50 AO IR
S410K .22 - Hawke Sport HD 3-9 x 50 AO IR
Logun Mk1 .22 - AGS 3-9 x 40
Theoben Taunus .22 - Simmons 4-12 x 40 AO
BW1911R2
Walther CP99
Webley Premier .22
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Re: Power Curves & the Sweet Spot

Postby Roger5 » Mon May 23, 2016 10:36 pm

Hi mark, let me know if you want a Robert Lane Reg, I have one that has never been fitted to a rifle, it's for S400 .177, will let you have it cheap. Rog
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Re: Power Curves & the Sweet Spot

Postby Mark112 » Wed May 25, 2016 7:42 am

PM sent Rog
S410C .177 Regged - MTC Viper 4-16 x 50
S410K .177 Regged - Hawke Nite-Eye 4-16 x 50 AO IR
S410K .22 - Hawke Sport HD 3-9 x 50 AO IR
Logun Mk1 .22 - AGS 3-9 x 40
Theoben Taunus .22 - Simmons 4-12 x 40 AO
BW1911R2
Walther CP99
Webley Premier .22
Mark112
 
Posts: 210
Joined: Mon Feb 16, 2015 5:25 pm
Location: Coventry

Re: Power Curves & the Sweet Spot

Postby oneshot99 » Tue Jul 05, 2016 10:57 pm

Interesting post, thank you
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Re: Power Curves & the Sweet Spot

Postby gdavison » Wed Jul 06, 2016 5:40 am

Great Article ... TY for sharing

With respect to the Scope height

Mark112 wrote:Scope height you will need to measure and is centre line of barrel to centre line of scope and is 1.6 inches on my .22. Zero range is obvious really and in my this case 25 yards. Ballistic Coefficient it taken from Chairgun's tables of data and for my air Arms Diablo Fields is 0.0310


The discussion started by BBF in this thread http://www.airarmsownersclub.com/viewtopic.php?f=5&t=3074 clears a confusion on that variable
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Re: Power Curves & the Sweet Spot

Postby Mark112 » Wed Jul 06, 2016 11:30 am

Hi,

Thanks. Yes been reading that thread and fully understand the issue. The problem is that the scope height is not really a fixed value but varies with the zero range and the angle of the barrel WRT the scope sightline. A good compromise is to say take 1.5mm from your measured scope height figure and use that. To be honest using the measured means an error of about 1mm at 50 yards and about 1.5mm at point blank. I may fire of a mail to Chairgun themselves to see whether this can be corrected in further versions of Chairgun. I have made comments before to them and they do take stuff on-board. It needs the end of barrel to scope measurement also to be entered to be accurate but I'm sure at one point this was a field in previous Chairgun versions.

Mark

P.S. Nice that someone read this thread :D

P.P.S As we have another thread on this subject you might like to follow this viewtopic.php?f=5&t=3074&start=10#p24781
Last edited by Mark112 on Fri Jul 08, 2016 8:49 am, edited 1 time in total.
S410C .177 Regged - MTC Viper 4-16 x 50
S410K .177 Regged - Hawke Nite-Eye 4-16 x 50 AO IR
S410K .22 - Hawke Sport HD 3-9 x 50 AO IR
Logun Mk1 .22 - AGS 3-9 x 40
Theoben Taunus .22 - Simmons 4-12 x 40 AO
BW1911R2
Walther CP99
Webley Premier .22
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Re: Power Curves & the Sweet Spot

Postby gdavison » Wed Jul 06, 2016 6:25 pm

Mark112 wrote:Hi,

Thanks. Yes been reading that thread and fully understand the issue. The problem is that the scope height is not really a fixed value but varies with the zero range and the angle of the barrel WRT the scope sightline. A good compromise is to say take 1.5mm from your measured scope height figure and use that. To be honest using the measured means an error of about 1mm at 50 yards and about 1.5mm at point blank. I may fire of a mail to Chairgun themselves to see whether this can be corrected in further versions of Chairgun. I have made comments before to them and they do take stuff on-board. It needs the end of barrel to scope measurement also to be entered to be accurate but I'm sure at one point this was a field in previous Chairgun versions.

Mark

P.S. Nice that someone read this thread :D


Mark - I really enjoyed reading the thread and appreciate all the work you put into it .. Many thanks :)

Re the measurements / techniques for scope height and "knock 1.5 mm off measured" I agree with your points .. reminded me of years ago doing my degree listening to a 2 hour lecture on Antenna design and radio and at the end my mate puts his hand up .. Prof says "you have a Q ?" Mate says "with such a complex subject can you explain why a coat hanger rammed in the remains of my snapped off car radio Ariel works ?" :D
AA S510 Ultimate Sporter .177 RatWorks Tuned - Hawke SW 4-16*50
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Re: Power Curves & the Sweet Spot

Postby Archer50 » Sat Aug 06, 2016 8:13 am

I've just found this thread, and just got my first unregulated gun :D. Thanks Mark, it's the clearest, most useful explanation of power curves I've seen, and I learned a lot from it.

Good shooting

Alan
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