laura888
Guest
Then I'll tell you first what I did:biggrin:.
in your parameters, every quarter of a turn the step increased like this:
pi; (pi+p)i=pi(i+i^2)...ecc, therefore, after n quarti of turn it was p(i+i^2+...+i^n) that in mathematical terms it is written pi^i^i.
At first I made the integral of a function f
=pi^n, which returns a growing function that approximates to your curve but, without stretching, it is not good.
then, as that sum is a elementary geometric progression, I simply got the sum
f=pi(i^n-1)/(i-1)
with n to 12a because it refers to quarters: 3giri*4=12.
in the excel sheet the x column shows the pi*d*n values, while the y column shows the values of that sum, which as you can see are the same as you got, except the last one you forced to 140
.
Let us now assume that at the first lap the desired quota is 14, to the second 49, to the third 140 (I make this example because in your file at the first lap you get 14.4 and to the second 49.6; 140 is the quota at the last lap);
In this case you can set a linear system of equations to find the coefficients of equation in n that I need (in this case n coincides with the num of revolutions.
This is something you can do relatively simple, maybe by setting a excel sheet.
But if you want to start from the total length of the curve (so from the measurement of the path), it seems a little more complicated.
Consider that, note the equation of a curve, in order to find its length you have to do all a bit of crap on which I do not dilute, which are not very simple. starting from the length and proceeding on the contrary it seems even more ostic and I do not have time to think about it.
I write you cmq an example of the equation found by imposing a fixed quota at each turn (it is any z(t)).
to write the equation in coord. cylindrical, consider that, unless you want a rake, r(t) is constant, so:
r(t)=raggio
θ(t)=360*t (it is the angle that sweeps the radius vector and then depends on how you change the t parameter, if t=n with n num turns, that's okay)
(c)(c)(c)(c)(c)(c))(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)
Attached files
Good evening
View attachment Elica p_var n3.zip
in your parameters, every quarter of a turn the step increased like this:
pi; (pi+p)i=pi(i+i^2)...ecc, therefore, after n quarti of turn it was p(i+i^2+...+i^n) that in mathematical terms it is written pi^i^i.
At first I made the integral of a function f
=pi^n, which returns a growing function that approximates to your curve but, without stretching, it is not good.then, as that sum is a elementary geometric progression, I simply got the sum
f
=pi(i^n-1)/(i-1)with n to 12a because it refers to quarters: 3giri*4=12.
in the excel sheet the x column shows the pi*d*n values, while the y column shows the values of that sum, which as you can see are the same as you got, except the last one you forced to 140
.Let us now assume that at the first lap the desired quota is 14, to the second 49, to the third 140 (I make this example because in your file at the first lap you get 14.4 and to the second 49.6; 140 is the quota at the last lap);
In this case you can set a linear system of equations to find the coefficients of equation in n that I need (in this case n coincides with the num of revolutions.
This is something you can do relatively simple, maybe by setting a excel sheet.
But if you want to start from the total length of the curve (so from the measurement of the path), it seems a little more complicated.
Consider that, note the equation of a curve, in order to find its length you have to do all a bit of crap on which I do not dilute, which are not very simple. starting from the length and proceeding on the contrary it seems even more ostic and I do not have time to think about it.
I write you cmq an example of the equation found by imposing a fixed quota at each turn (it is any z(t)).
to write the equation in coord. cylindrical, consider that, unless you want a rake, r(t) is constant, so:
r(t)=raggio
θ(t)=360*t (it is the angle that sweeps the radius vector and then depends on how you change the t parameter, if t=n with n num turns, that's okay)
(c)(c)(c)(c)(c)(c))(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)(c)
Attached files
Good evening
View attachment Elica p_var n3.zip