We need more information like what are your RPMs doing during the "shot"....coming up slowly, steadily, as the boat picks up speed, or jump up to like 3k right off and just keeps increasing to your 7k top end number? You quoted speed numbers but were they actual or WAGs?
To get some hard numbers in an attempt to answer your questions, we need: Engine RPM, prop pitch, indicated speed, and gear ratio. With firm numbers one can calculate prop slip and get an idea as to whether or not things make sense and if not, where to look for the source of the problem. There are prop slip calculators online; Mercury or Go-fast.com are two sources but you need to know the gear ratio of your lower unit to use them. They are a big help in understanding where you are but need data to work.
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My association with Mercury engines is that the serial number and model information are on a weather resistant decal placed on the transom clamp bracket easily viewed from the right (starboard) side of the engine while at the rear (stern) of the boat. My association with the Welch plug is with the cowling off, standing on the left (port) side of the engine, at the transom, one would look for an aluminum (round) disc, mounted in an alcove in the engine block about the size of a US quarter dollar coin, would contain the serial number. If you find the alcove, with the plug missing, then it has also been removed and one has to suspect that the engine is as specified.....which is another subject.
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The last three characters on your prop tell me that its 19P, 19" pitch, moving forward 19" per revolution if a screw turning in wood. In water there is slip involved and it doesn't move the same distance per rev. as in a solid, as the prop is stamped. We'll assume that your tach is telling the truth, but it may be set to the wrong number thus counting more RPMs that actually exist....setting on the rear of the unit and correct setting per engine used is in manufacturer's data, sometimes published online. At 7k RPMs, your engine would be screaming.....BTDT, but if the prop is ventilating at WOT it could happen.
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Your "hole shot" comments, assuming that you "firewalled" the throttle for the shot, "seem to indicate" too much pitch or not the right trim angle for the "rig" (boat, engine, setup, load and distribution). Decreasing pitch (having correct engine height) would go to correct that, or using a prop with "ports" like a Mercury Laser II to name one of many, which have the same effect as having a lower pitched prop durning the shot.
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Since you have no engine ID, you can figure out your gear ratio by pulling the spark plugs to reduce drag, mark a spot on the flywheel against a fixed object and mark the propeller against some fixed object. In F gear, rotate the flywheel, keeping track of movements until the prop has completed one 360* revolution. Measure the amount of flywheel rotation. My records indicate that engines of that size of the day were running 1.75:1 or 1.87:1 gear ratio, meaning that the power head turned that many turns for one complete revolution of the prop. If you don't have a "Protractor" $ General sells them with a "compass circle drawing instrument" in a package for a few bucks. Figuring the angle on the second rotation, it's .75 x 360* or .87 x 360* for the angle to measure in getting your number.
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I agree that your engine may be too high on the transom and you are "ventilating" at high rpms. This could manifest itself it your hole shot fails the rpm test I mentioned earlier. Some pictures would help like a side view with a yard stick up against the hull at the transom, extending on back past the engine, with the engine in a vertical position with the boat level on the trailer. Also a rear view looking straight at the stern, engine vertical as before, taken with the camera about a foot and a half to two feet off the ground.
Give us that and your gear ratio, answering the question as to the actual speed vs what you posted and we can go from there.
