Yes it does matter if your barrel is hot after your cold bore. You should notice some type of change in the POI after your first shot. Some rifles are more drastic than others. Well made rifles with custom barrels generally will hold their point of aim.
With that said. I like to wait 2 to 10 mins between shots for load development to maintain a consistent barrel temp. I think this helps to maintain a better group. I know that temps will cause groups to open up. The time is determined on the temperature of the day. This what I do, others will have there own methods.
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I haven't seen but a few rifles that have a cold bore POI change, or one thats worth worrying about. Sometimes I think it is the shooter that causes the first round flier. If your rifle seems to have a cold bore POI change, try dry firing for several minutes befor loading a round in the chamber or let somebody else shoot it first to eliminate the human error. Then if you do have a POI difference you need to make sure it is consistant as well and to the same POI. Then just anotate it and adjust for follow up shots.
The biggest problem I've seen is guys cleaning their rifles after every trip to the range and then waiste several shots to get it to calm back down. I use to clean my rifles after every trip but now let the rifle tell me when she needs a cleaning, even my issued M24.
Before I ever start my group I set up another target and shoot 2 fouler shots this does two things 1. It of course fouls out the barrel and 2. it brings the barrel up to temperature after that and then only, I start my 5 shot or 10 shot group If I clean my barrel I will repeat this process try it you'll be amazed . Note I would not clean my barrel then go hunting without it being fouled out again . I used to clean clean befor opening day and then rush off to hunt not anymore alote of folks in competition do it this way.
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Most F class and Palma shooters shoot 15 (or 20, depending on the competition) rounds for score in 22 minutes, at 800, 900, 1000 yards, so distances comparable with what long range hunters shoot.
If you calculate that you usually make your read, shoot a few sighters, then settle in for the shots for score, your 15 shots are usually done in no more than 15 minutes, and typically in 10 or less if your target puller is fast.
The barrel heats up, but I've not seen anyone make adjustments for that heating, nor do I. A well made rifle with a heavy barrel shouldn't change much.
Some of the thin, hunting weight barrels might be more affected, but I have no experience with using those for extended strings.
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Re: Time between shots
Due to a large case capacity, I let 3 minutes pass between shot one and shot 2 and 4-5 minutes between shot 2 and 3 in my 338 EDGE barrel. I do this to help save the barrel. So far after 100 rounds, the throat and barrel look brand new with not a single heat crack in the barrel. This is the only reason I do this.
With my 308 I will fire 1-5 at a normal pace whether it is practice or developmental.
Each rifle will be different. Some rifles will just NOT put bullet #1 in the group from a cold bore even if it is 60+ degrees outside. Most rifles when it is above freezing will put 1-3 (for a skinny barrel and 1-5 in a heavy barrel) in the same group. With most rifles the cold bore shot means little unless the barrel is very cold. Then #1 typically wont go in the group. The colder it gets, the worse it gets. Almost all rifles will suffer some kind of bullet #1 POI shift when it gets cold enough. I think it is even safe to say all barrels will suffer a POI change given enough temprature drop.
You will have to test your rifle to see at what point bullet #1 wont stay in the group. This time of year, I suspect you wont have to worry about it.
Long range shooting is a process that ends with a result. Once you start to focus on the result (how bad your last shot was, how big the group is going to be, what your buck will score, what your match score is, what place you are in...) then you loose the capacity to focus on the process.
depends on the rifle.
for my heavy barrel 223 i will shoot my 5 shot group and do it in whatevre time i feel like. not very scientific but when i go shoot gophers i don't wait several minutes beteeen shots. sometimes it's 5-10 in the space of 5 minutes then i'll sit for 10 minutes?
i don't clean between groups unless i change powder, again what's the point?
for my 6.5x55 it gets much hotter with a 1/3 of the shooting so i do take my time so i don't wear out the barrel. it's my long range varmint/predator rig so i might take 3 shots quick then hold off till the barrel cools and finish the 5 shot group.