Trig Help - Sphere seated in Cone

[[Ri...]]

I had someone help me with this years ago, and now I'm struggling.

I have a 120° Cone that I need to calculate the height of a theoretical sphere (3") seated into it. The only part of the equation that I remember is that you have to start at the origin of the cone (or that was how this particular person calculated it).

I do not want to use lines and a tangent construction - I want to be able to calculate it directly from the cone.

Any and all help is greatly appreciated.

[[Ow...]]

I often keep notes of things I think I might need one day and found this.

Gauge Ball in Cone Formula:
measure the cone
open result element
right click in the formula field and select formula
((cos(half cone angle)*(gage ball radius) * 2 open cone calculation
check Position definition
right click and select formula
select (result element get actual result) + ((sin(half cone angle)) * gage ball radius) + gage ball radius

[[Ri...]]

Hmm. The value that I am getting is not correct.

[[Cl...]]

Should be 1.73204" From the apex. I think my math is correct?

[[Ri...]]

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Owen,

I don't know why, but mine works out differently. Another thing I learned is that I have to use the Deg function, and for whatever reason Calypso wouldn't pull the angle from the feature directly, so I had to create the half cone angle characteristic.

Here are the steps that I had to use to get the correct answer.

In Calypso 2021:

Create a Half Cone Angle Characteristic for your Cone

Create a Result Element and use the following formula:
((cos(deg(getActual("Half Cone Angle1").actual))*Gage Ball Radius)*2)

Create a Cone Calculations Feature, select Position Definition, and use the following formula:
(getActual("Result Element1").actual) + ((1/cos(deg(getActual("Half Cone Angle1").actual)))*Gage Ball Radius)+Gage Ball Diameter

[[Te...]]

Let me know if this document helps

Over Ball Height.pdf

[[Ri...]]

That works perfectly. Thank you.