Archemedies Spiral

by rhimmelblau
Tags: archemedies, spiral
rhimmelblau is offline
Nov28-12, 11:28 AM
P: 7
Hi I'm working on a project where I need to develop a flight path to cover a circular area. I was thinking of having the plane follow an archenemies spiral. I found that the general equation in polar is r=a(theta)^1/n
My question is if I have a specific distance I want each spiral to be from the last how do I input that into the equation.
Also is there a Cartesian equation for the spiral?
Edit: Also how does one calculate the arc length of the spiral?
Phys.Org News Partner Science news on
Cougars' diverse diet helped them survive the Pleistocene mass extinction
Cyber risks can cause disruption on scale of 2008 crisis, study says
Mantis shrimp stronger than airplanes
tadchem is offline
Nov28-12, 12:29 PM
P: 61
The equation for the Archimedes spiral is:
R = a*theta
Each turn is separated from the last (and the next) by a distance (measured radially) of
d = a*(2*pi)
There is no Cartesian Equation because it is not a single-valued function in cartesian space; there is no single value of x (or y) that can be associated with a given value of y (or x).

P.S. Don't tell your archenemies. Make them figure it out for themselves.
rhimmelblau is offline
Nov28-12, 01:29 PM
P: 7
So if I have a radius that I need to search and a distance each successive turn should be from the last, then I can use the arc length equation s=0.5*a[theta*sqrt(1+theta^2)+ln(theta+sqrt(1+theta^2))].
So I would plug in "a" equal to my distance/2*pi,
Then theta would be how many turns I go around the circle, which I can find by adding up the incremental distances between the spirals until I reach the radius of the search area.

Correct me if you see any flaws in my logic.

Register to reply

Related Discussions
Archemedies principle Introductory Physics Homework 9
The Odd Only Spiral (A twist on the ulam spiral with an interesting property) Linear & Abstract Algebra 9
Bee and a spiral Introductory Physics Homework 3
Finding the spiral sinks and spiral sources of a linear system Calculus & Beyond Homework 3
3D Spiral.. Please help me out Calculus 1