Cross Vertical Staff Model for School Maths Lab

Quick Answer: Cross Vertical Staff Model for School Maths Lab is a model of the surveyor’s cross staff, a sighting head mounted on a vertical staff and used to set out lines at right angles on the ground. Maths classes use it to take offsets and find the area of irregular plots of land.

How a Cross Staff Sets Out Right Angles

A cross staff is one of the simplest surveying instruments. Its head carries two pairs of sighting slits at right angles to each other, and it sits on top of a pole that is pushed into the ground so that it stands vertically. Sighting along a straight chain line through one pair of slits, the surveyor then looks through the other pair, which points exactly at right angles to that line. Any object seen through the second pair lies on a perpendicular from that point.

In a school maths lab the model supports the classic method for finding the area of an irregular field. A long baseline is laid across the field, and from points along it the cross staff is used to set out perpendicular offsets to each corner of the boundary. Recording the distances along the baseline and the offset lengths in a field book divides the field into right-angled triangles and trapeziums, whose areas students calculate and add.

Doing this outdoors, even on a school ground or a playground marked with chalk, shows students why the formulas for the areas of triangles and trapeziums matter. The model’s material, height and sighting arrangement should be confirmed before ordering; a measuring tape and ranging rods or markers are needed alongside it.

Applications

• Setting out right angles on the ground from a straight baseline
• Taking offsets to the corners of an irregular plot
• Keeping a field book and computing area from triangles and trapeziums
• Outdoor mensuration projects on the school ground

Specifications

Care & Handling

• Keep the sighting slits clean and undamaged; a bent slit throws off the right angle.
• Wipe off soil after outdoor use and dry the model before storing.
• Carry the staff upright and close to the body between stations, and store it where it cannot fall.

Why Choose LabEquip

Maths and geography teachers who take mensuration outdoors buy a cross staff with a tape and markers, and the Clinometer Compass extends the same fieldwork to heights and bearings. Both are in LabEquip’s Mathematics School Lab Products range; send your requirement through the contact page.

Frequently Asked Questions

What is a cross staff used for?

Setting out lines at right angles to a main survey line. Surveyors use it to take offsets, the perpendicular distances from the chain line to features such as the corners of a field boundary.

How do you check that the cross staff gives a true right angle?

Set it up, sight a mark along the chain line and a second mark through the cross slits. Turn the head a quarter turn so the slits swap roles; if the same two marks line up again, the right angle is true.

How is the area of an irregular field found with offsets?

A baseline is laid across the field and offsets are taken from it to each corner, dividing the field into right-angled triangles and trapeziums. Their areas, from half base times height and half the sum of the parallel sides times the distance between them, are added.

What is a field book?

A record of the survey, usually drawn as a column for distances along the baseline with offsets written to its left or right. Students use it later to draw the plot to scale and calculate its area.

Why must the staff stand vertically?

The sighting head only gives a true right angle on the ground when the staff is upright and the slits are level. Check it by eye from two directions, or against a plumb line, before sighting.

Can the model be used indoors?

It can be demonstrated in a hall or corridor with a chalk baseline and markers, which is useful before an outdoor lesson. The full offset survey needs open ground where students can lay out a baseline and walk to the corners.

Last Updated: September 2026