Calculating Height For Desired Angle of Cone.

[Beale]

A bit of a mix between very basic modelling and (presumably) very basic math question (But, Google searching has not helped me so much). Sorry if I have missed some basic links to this.

In a nutshell, I would like to model several conical parts that all maintain the same angle. For each model, the calculation boils down to this:

So, for a known angle (Here 56°), top diameter a and bottom diameter b: can I calculate the height needed to deliver this angle on the side?

Some example, top diameter is 1.25m, bottom diameter is 2.5m, how can I calculate the needed height for 45 degrees slope on the side?

Thanks & Kind Regards.

[hraban]

Hi,

with given

angel b = 56°

length of side y = 0.625 (1/2 of difference between nodes)

angel c = 90°

you become a high of 1.118

take this one: http://www.calculator.net/triangle-calculator.html?vc=90&vx=&vy=0.625&va=0&vz=&vb=56&angleunits=d&x=65&y=13

[Beale]

Hi,

with given

angel b = 56°

length of side y = 0.625 (1/2 of difference between nodes)

angel c = 90°

you become a high of 1.118

take this one: http://www.calculator.net/triangle-calculator.html?vc=90&vx=&vy=0.625&va=0&vz=&vb=56&angleunits=d&x=65&y=13

Thanks!

But, what is the calculation?

The online tool restricts to three decimal places so isn't quite accurate enough

For example, calculations for 1.875m > 2.5m cone delivers height of 0.463(trucated) and angle of 56.2

[maltesh]

A 45° slope is exactly as high as it is wide.

So in the case of the 45° slope, the height is /exactly/ (b-a)/2.

If the angle between the Base and the slope is θ,

then the height (h) is h = 0.5*(b-a) tan θ

Keep in mind that most online calculators will assume you're using radians for your angle, so if you're using something like Google or Wolfram Alpha to do the calculation, and your angle is in degrees, you'll have to explicitly declare that, or do the conversion.

Your posed problem works out to 0.927 m, if rounded to three significant figures.

Edited October 31, 2015 by maltesh

[Beale]

A 45° slope is exactly as high as it is wide.

So in the case of the 45° slope, the height is /exactly/ (b-a)/2.

If the angle between the Base and the slope is θ,

then the height (h) is h = 0.5*(b-a) tan θ

Keep in mind that most online calculators will assume you're using radians for your angle, so if you're using something like Google or Wolfram Alpha to do the calculation, and your angle is in degrees, you'll have to explicitly declare that, or do the conversion

Exactly what I needed!

Many thanks for the info.

[hoojiwana]

Are you modelling that MAV thingy? The way I would do this is to make one big cone, loop cut the segments I want into it, separate them and fill the gaps.

[Beale]

Are you modelling that MAV thingy? The way I would do this is to make one big cone, loop cut the segments I want into it, separate them and fill the gaps.

http://i.imgur.com/LBZPry4.jpg

You are spot on the money yes, for the MAV thing

Cutting it this way is another viable option too, thanks!