Is there a way to compare your static hold and one rep-max record? Is there a way to find out what your one-rep max is from your static hold record/measurement and vice versa?
For example, if you can manage to hold a plank for 5 minutes, can you estimate how long you'd be able to hold a plank with an additional 15 lbs on your back?
No, there is unfortunately no such formula.
But I am going to go further and make a stronger claim: there will never be such a formula! The reason is that the correlation between repetitions and time-under-tension is very poor, and it is even poorer when we compare isotonic contraction with isometric exercise.
Suppose, for example, that we were able to perform 60 push-ups in 60 seconds. In order to achieve that objective, we would be required to perform one push-up per second, during which time we would have to brake the fall of our mass to the floor and accelerate it back to the starting point with arms fully extended. This rapid cycle of negative and positive accelerations, respectively, demands that we produce forces far greater than the relevant component of our body weight. Hence, the more slowly we perform the movement, the closer our effort approaches to our weight. That is, the more slowly we do our push-ups, the less force we have to produce in doing them.
So suppose, instead, that we decide to perform the push-ups more slowly, hence moderating the force required for each repetition—the idea being that we should fatigue more slowly, and thereby be able to perform more repetitions in total. This causes another problem: our muscles are now under tension for a longer period of time, requiring muscular effort.
In practice, changes to our rate of repetition makes very little difference to the total number of repetitions we can perform. In the above example, even with a reduction in rate of 20 or 30 per cent, we would likely perform only two or three repetitions fewer! Similarly, the strength that we can demonstrate in an isotonic contraction has very little bearing on how long we can hold a sub-maximal isometric contraction.
The length of an isometric hold appears to be related far more closely to our total energy consumption than it does to the physical work we perform. Indeed, isometrics are essentially a distinct physical skill, and one which cannot be compared meaningfully with isotonic contractions.
I hope that helps.
I've scoured the web to find an answer to this, as static strength is its own science, this is quite a difficult concept. I did find out there is a relationship to rate of force development, and explosive strength, since they all involve single contractions of the muscle. There are also multiple types of isometrics, such as overcoming isometrics and yielding isometrics, or even ballistic training. Your question seems to be aimed at yeilding isometrics(holding a weight). It's not a linear formula, for instance, if you plank for 5 minutes, 10 pounds on your back could reduce that to 2.5 minutes, or maybe 4 minutes, it depends on your static strength.
according to T-nation, a load of 50 to 80% for a duration of 20 to 60 seconds is best for hypertrophy. Everything is based off a 1-rep max, so planks might be hard to calculate but an isometic bench press, just take your 1-rep max, for instance, 250, and 50% would be 125lbs for 60 seconds, or 80% would be 200lbs for 20 seconds. so for 250 lbs 1 rep max, 125 for 60 seconds on the high end, 200 for 20 seconds on the low end. Try adding weight to a plank and see how much weight you can hold for 2 seconds, which is when "peak force of development" occurs, so you can definitely hold for 2 seconds.. you could use this as your 1 rep max, and use the same percantages, lets say you can do 100lb 2 sec max.. 50 lbs could be done for 60 seconds, or 80 lbs for 20 seconds. According to the research done by this article, https://www.t-nation.com/training/isometrics-for-mass, you should only do 20-60 seconds for maximal hypertrophy.. anything more is not beneficial, depending on your goals.
overcoming isometrics is trying to push weight that you impossibly cant move, but it stimulates muscle growth either way.. try pushing a car for 6 seconds.. you cant move it but you can gain muscle growth. This doesn't apply here but the weight doesn't matter.
To summarize, 50% of 1rm for 60 seconds or 80% for a 20 seconds. Anything more than 20-60 seconds is not hypertrophy but a combination of joint strength, tendon strength, explosiveness and speed. If you need an exact formula, I'm sure a skilled Health scientist/mathematician could use the rate of force formula against isometrics to calculate a length, but other than some estimations done by bodybuilders, there is not an EXACT formula for this, but really an estimation.
