Step 33 – Calculating Lock-Time
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Compared to other forms of shooting, lock-time (LT) isn’t as paramount in benchrest. Think about off-hand for a moment. There, high duration increases the risk of movement and by lowering LT accuracy usually improves. BR works off of fixed tops and rigid bags though. Firm bases and the free-recoil style so many embrace makes it less important on actions like ours. Even so, it can’t be ignored completely.
Lock-time is an idea thrown around a lot on the internet. Great discussion, but I often wonder if folks understand it in its entirety. For example, one guy argued trigger pull is the main driver. Another claimed heavy revolver hammers cause faster fall. Incorrect as that may be, there’s a lot to consider when figuring lock-time. Enough so that I thought it would be good to share the full computation. This piece focuses on bolt actions but in time I’ll do a revolver derivation.
By definition, lock-time is the interval between sear release and primer strike. Trigger travel and internal movement are other elements I’ll discuss later.
Let’s start with the main measurements:
FL = total length of the uncompressed mainspring (3.750)
L0 = length of the compressed and cocked spring (2.125)
L1 = spring length in the fired position (2.375)
X0 = spring compression when cocked (1.625)
X1 = spring compression when fired (1.375)
FPT = firing pin travel (0.250)
Fpt = firing pin travel to the primer (0.195)
We’ll also need the mainspring’s rate (K) in ft/lbs and the mass of the moving parts (M) in lbs-sec2/ft.
LT = [(cos^-1(L1/L0))/Sqrt(K)] x Sqrt(M)
Insolating each input:
X0 = FL – L0……3.750 – 2.125 = 1.625
X1 = X0 – FPT……1.625 – 0.250 = 1.625 – 0.250 = 1.375
The mainspring rate is less straightforward. To calc it these are a must:
D = the wire diameter
OD = outside diameter of the spring
R = mean radius of the helix
N = active number of coils
Our spring is 0.056” in wire diameter and 0.409 OD. It also contains 23 active coils. The radius is figured as follows:
R =1/2(OD – d) = 1/2(0.409 – 0.056) = 0.1765
Knowing steel’s modulus of elasticity, K is:
K = (D^4 x 11,500,000) / (64 x R^3 x N) = (0.056^4 x 11,500,000)/(64 x 0.1765^3 x 23) = 13.97 lbs/in
Converting to lbs/ft = 167.68 lbs/ft
The weight of the firing pin, cocking piece, and spring is 0.112 lbs. Dividing by earth’s gravitational constant yields mass:
M = (0.112 lbs) / (32 ft/sec2) = 0.0035 lb-sec2/ft
We can now calculate lock-time:
LT = [(cos^-1(2.375/2.175)/Sqrt(167.68)] x Sqrt(0.0035) = 0.00253 or 2.5 milliseconds (ms)
Is 2.5 ms good or bad? Well, 2.0 is deemed fast and aftermarket kits like David Tubb’s Speedlock approach that number; achieving less is tough. Old military rifles like the 1903 Springfield and Mauser 98 had from here to eternity LT’s, usually 6.0 to 9.0 ms. Most modern bolt actions land between 3.0 and 4.0 with their in-line springs. Non-linear ignition systems have much higher durations, 30 ms to over 100 ms in the case of revolvers. Ever wonder why single-actions can be harder to master than double-actions? Factory Ruger Blackhawks drop in 75 ms whereas Smith & Wessons are around 40 ms. That’s a sizeable difference.
Does 2 ms saved in a bolt action matter? For off-hand it does, but is anything gained on a benchrest gun? Human reaction spans 150 – 300 ms, many orders higher than my firing assembly. You’d think even a 10 ms lock-time would be nullified by the shooter. Not so. Remember, human reaction measures the interval between the conscious decision to act and the act itself. In shooting, that’s the time from deciding to pull the trigger to your finger being depressed. Once the sear releases, the ensuing mechanics are out of your control (though you can move the stock inadvertently thus effecting the shot). But assume you don’t influence the gun as is the case with free-recoil benchrest. In that scenario you simply touch the trigger and no other part of the gun. A chain of events takes place in the rifle and culminates with the bullet exiting the barrel. Throughout lock-time, vibrations and faint muzzle movements occur. They cannot be entirely eliminated. So lowering the void between sear release and primer strike reduces movement opportunity. Again, a millisecond here and there doesn’t payoff in benchrest like it does in other shooting forms. It is valid though when trying to eke out a hundredth or two in precision.
To summarize, lock-time can be shaved by:
1) Lightening the mass of the pin assembly
2) Increasing the mainspring rate
3) Decreasing the total travel
It's also good to understand the impact energy on the primer:
E = [(F0 + F)/2] x fpt
F0 = initial mainspring load = (K) x (X0) = 13.97 x 1.625 = 22.77 lbs
X’ = mainspring compression at fpt = X0 – fpt = 1.625 – 0.195 = 1.430 in
F1 = final mainspring load = (K) x (X’) = 13.97 x 1.430 = 19.98 lbs
Notice how the calculated initial load of 22.77 is very close to our scaled figure of 23?
E = [(22.77 + 19.98)/2] x 0.195 = 4.2 inch pounds
A stock Remington puts 5.0 to 5.5 inch-pounds of impact energy on the primer. Lab tests have found most rifle primers, to include thicker cupped BRs, only need 2.5 inch-pounds to ignite consistently. This is relevant for two reasons:
1) Our action has a lower lock-time than factory 700’s (it’s on par with the Tubb’s Speedlock)
2) Our impact energy is 25% less but still well above the minimum.
Lower lock-time reduces the window for vibrational interference. Lower impact energy also cuts vibrations across the receiver and barrel post-strike. The formulas show we achieved the best of both worlds – short lock duration without excessive primer hit. So how did we accomplish that? While our spring load is less than a Remington, we also cut the pin travel (0.250” vs. 0.270” on the 700). That shorter distance, while seemingly small, permits us to use less spring. Namely 5 lbs lower on the compressed load. A lock-time of 2.5 ms is fast enough, there’s no call for additional force. The reduction in LT would be immaterial and the uptick in strike energy would be unneeded. Harder impact also means bigger vibration and that’s a group killer. It’s no wonder the BR crowd avoids overly heavy springs.
-Lee
www.singleactions.com"Building carpal tunnel one round at a time"