How to simplify the calculation of the solenoid / solenoid valve?

Question

Electronics

Good afternoon.
I am making a solenoid valve, you need to calculate which coil (how many ampere-turns) is enough to confidently retract the piston (movable armature). In one of the many textbooks I found the formula:
F = (nxi)2 x magnetic constant x S / (2 x lav2)
Where
F = Force,
i = Current,
lav = The length of the gap between the solenoid and a piece of metal,
S = The cross-sectional area of ​​​​the electromagnet
n = Number of turns,
Magnetic constant = 4 x PI x 10^-7.
I expect:
I=0.3A
S=0.000136 sq.m.
N=3000,
Lav=0.001m
It turns out 69 Newtons or 7 kilograms!
I don't think something is right here...
How big is the discrepancy from reality (2-1000 times?)? In general, does it make sense to use it for at least an approximate calculation?

Answer 1

It is also worth considering what material the magnetic circuit of the coil and the so-called armature are made of.
And also a significant role is played by the distance at which the anchor is initially inserted into the solenoid.
Once upon a time, there were scripts for a program that simulated the retraction of a rod into a Gaussian solenoid per millisecond. You can dig in that direction on the specialized forums.