Descriptive Geometry: True Length of a Line

≈ 38 min

Descriptive Geometry: True Length of a Line

A line in space appears true length in a view only when it is parallel to that view's projection plane. If a line is inclined to both the HP and the VP, neither the plan nor the elevation shows how long it really is — both show it shorter.

The standard construction is rotation: rotate the line in the plan until it is parallel to the VP, project the rotated position up to the elevation, and measure there. The rotated line is now parallel to the projection plane, so its projection is true length.

The line's inclination — the angle it makes with the HP or the VP — appears in the same view where its true length appears, measured against the ground line.

Worked example. A roof hip runs diagonally in plan and rises as it goes. Its plan length understates it (it ignores the rise) and its elevation length understates it too (it ignores the diagonal run). Only the rotated view gives the length of timber to cut.

Core checkpoint: True length and true inclination appear together, in the view where the line is parallel to the plane.

When does a line appear at its true length in a view?

When it is parallel to that view's projection plane.

When it is perpendicular to that view's projection plane.

When it passes through the ground line.

Whenever it is the longest line in the view.

A line is inclined to both the HP and the VP. What is true of its plan and elevation lengths?

Both are shorter than the true length.

The longer of the two is the true length.

The plan always gives the true length.

They are equal to each other and to the true length.

In the rotation method, what is done to the plan of the line?

It is rotated about one end until it lies parallel to the ground line, then projected into the elevation.

It is extended until it meets the ground line.

It is bisected and each half projected separately.

It is redrawn at double scale.

A roofer measures a hip rafter from the roof plan alone. Why will the timber be cut too short?

The plan shows only the horizontal run and ignores the rise, so it understates the rafter's true length.

The plan is always drawn at a smaller scale than the elevation.

The plan exaggerates the length, so the timber would be too long.

Roof plans do not show hips at all.