Boom radius and tip height

R 03 mHow it works

Radius and height:   R = foot offset + L × cos A
                     H = foot pin height + L × sin A
Length and angle:    L = √((R − foot offset)² + (H − foot pin height)²)
                     A = atan2(H − foot pin height, R − foot offset)
Indicator range:     R at A − 2° and at A + 2°

A straight boom is the hypotenuse of a right triangle. Its foot pin sits a little behind or ahead of the centre of rotation and some way above the ground; its tip is out at the radius and up at the tip height. For a straight boom of length L at angle A from horizontal, radius is about L × cos A plus the horizontal offset of the boom foot from the centre of rotation, and tip height about L × sin A plus the foot pin height¹.

Radius and height mode runs that forward: give it the boom length and angle, and it returns where the tip is. Boom length and angle mode runs it backward: give it the point the tip has to reach, and it returns the shortest straight boom that reaches it and the angle it would sit at.

The indicator range. IHSA states that boom angle indicators can be off by as much as 2 degrees and should not be relied on for critical lifts; a measured radius is preferred¹. The tool works out the radius at your angle minus 2° and plus 2° and shows the range. On a long boom at a low angle, 2° moves the hook a long way.

The drawing beside the result is to scale for the numbers you enter, with the truck shown schematically. It is there to check that the geometry matches what you have in mind: the foot pin height and offset come from the truck's dimension sheet, not from this page.

R 06 mAssumptions and sources

• Under load the boom and the machine deflect, and IHSA notes the radius grows as a result¹. The radius here is the unloaded geometry, so the loaded radius will be larger.
• Load radius on a chart is the horizontal distance from the crane's centre of rotation to the load hook while the boom is loaded¹. That is the number to compare with the chart, and it is best measured on site.
• The default foot offset (0 m) and foot pin height (2.5 m) are examples, not typical values. They vary from truck to truck.
• Tip height is the height of the boom tip, not the hook. The hook block, the slings and the load hang below it; the size estimator adds them.
• Being out of level changes the radius and the capacity. In IHSA's example table, a long boom at minimum radius lost 30% of chart capacity at 1 degree out of level¹.

R 09 mUsing the answer

Use the result to describe the job, not to set the boom. If you are asking for a quote, the useful numbers are the radius and the tip height the work needs, plus the weight on the hook; "Get this priced" carries the radius and height into the request. A supplier then checks their truck's chart at that radius, over the quadrant you will lift in. Capacity is normally greatest over the rear, less over the side and may be nil over the front¹.

If you are comparing trucks, remember that a longer boom is not automatically better. The same radius can be reached by a shorter boom at a lower angle or a longer one at a higher angle, and the chart figure differs between the two. Ask for the chart, not the boom length.