# Builder's Old Measurement

Builder's Old Measurement (BOM, bm, OM, and o.m.) is the method used in England from approximately 1650 to 1849 for calculating the cargo capacity of a ship. It is a volumetric measurement of cubic capacity. It estimated the tonnage of a ship based on length and maximum beam. It is expressed in "tons burden" (Early Modern English: burthen, Middle English: byrthen), and abbreviated "tons bm".

The formula is:

${\displaystyle {\text{Tonnage}}={\frac {({\text{Length}}-({\text{Beam}}\times {\frac {3}{5}}))\times {\text{Beam}}\times {\frac {\text{Beam}}{2}}}{94}}}$

where:

The Builder's Old Measurement formula remained in effect until the advent of steam propulsion. Steamships required a different method of estimating tonnage, because the ratio of length to beam was larger and a significant volume of internal space was used for boilers and machinery. In 1849, the Moorsom System was created in Great Britain. The Moorsom system calculates the cargo-carrying capacity in cubic feet, another method of volumetric measurement. The capacity in cubic feet is then divided by 100 cubic feet of capacity per gross ton, resulting in a tonnage expressed in tons.

## History and derivation

King Edward I levied the first tax on the hire of ships in England in 1303 based on tons burthen. Later, King Edward III levied a tax of 3 shillings on each "tun" of imported wine, equal to £108.95 today (using the last year of Edward III's reign, 1377, as the base year). At that time a "tun" was a wine container of 252 gallons weighing about 2,240 lb (1,020 kg), a weight known today as a long ton or imperial ton. In order to estimate the capacity of a ship in terms of 'tun' for tax purposes, an early formula used in England was:

${\displaystyle {\text{Tonnage}}={\frac$

where:

• Length is the length (undefined), in feet
• Beam is the beam, in feet.
• Depth is the depth of the hold, in feet below the main deck.

The numerator yields the ship's volume expressed in cubic feet.

If a "tun" is deemed to be equivalent to 100 cubic feet, then the tonnage is simply the number of such 100 cubic feet 'tun' units of volume.

• 100 the divisor is unitless, so tonnage would be expressed in 'ft³ of tun'.[1]

In 1678 Thames shipbuilders used a method assuming that a ship's burden would be 3/5 of its displacement. Since tonnage is calculated by multiplying length × beam × draft × block coefficient, all divided by 35 ft³ per ton of seawater, the resulting formula would be:

${\displaystyle {\text{Tonnage}}={\frac$

where:

• Draft is estimated to be half of the beam.
• Block coefficient is based on an assumed average of 0.62.
• 35 ft³ is the volume of one ton of sea water.[2]

Or by solving :

${\displaystyle {\text{Tonnage}}={\frac$

In 1694 a new British law required that tonnage for tax purposes be calculated according to a similar formula:

${\displaystyle {\text{Tonnage}}={\frac$

This formula remained in effect until the Builder's Old Measurement rule was put into use in 1720, and then mandated by Act of Parliament in 1773.