How did You come up with these figures ?
It is a calculus math problem but there are many sites on the internet where this information can be found. I have a book by Cooper Bussmann at school that I use in the class for fuses. I also use the Square “D” trip curve booklet for breakers.
Fuses and breakers are used to protect electric motors along with running overload protection that is either internal or separate of the motor. Motors in AC and heat pumps will have running overload that is internal the motor and auto reset while motors like garbage disposals will have manual reset overloads.
Look at your AC or heat pump and find the minimum circuit ampacity. This is used to size the circuit conductors.
Now find the maximum fuse or HACR overcurrent device. This is what we use to size the fuse or breaker with.
The overcurrent protective device will always be larger than the circuit conductor ampacity. The reason is because for the compressor to start it must overcome locked rotor ampacity.
Looking at Table 430.248 of the NEC we can see that the running ampacity for a single phase 5 horse power motor at 240 volts is 28 amps. Table 430.52 says that the inverse time breaker (breakers sold at the supply house, HD, Lowe’s ect) is to be sized at 250% or a 70 amp breaker. Why? Because the breaker must hold until the locked rotor ampacity is over come and the motor reaches full speed.
Look at Table 430.251 and we will find that this motor will have a locked rotor ampacity that is six times that of the running ampacity or amperage of 168 amps. The breaker must hold this inrush current until the motor reaches full speed. Under load this can take several seconds.
Using this same rule of thumb we can apply it to the breakers in our home. It will not work out to the exact number as the calculus math but will be real close.
This same method is used in drivers education. Take the speed of your car and divide by 2 then add it back to the speed to see how many feet per second you are traveling. Example; At 60 miles per hour divided by two is 30, added back to 60 equals 90 feet per second but calculus figures to 88 feet per second.
A non-time delay fuse on the other hand is a lot quicker to open.
Edited to add:
In most cases during a fault condition most breakers will open between 120 and 180 cycles or two to three seconds.
While teaching at DCC we did a test using a GE 20 amp breaker and a very large rheostat. We loaded the breaker to 30 amps for over two minutes before it opened. We loaded the same breaker to 120 amps and it took just under 10 seconds but over 9 seconds to open. (The watch had 10.2 seconds but we subtracted the reaction time to operate the stop watch)
We did the same test using Square “D” home line and Siemens breaker with similar results.