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Let’s return to the Royer Nelson formula to consider one of the most significant findings about how much water is needed to fight confined structure fires. This is the discovery that two different research projects in different countries, 36 years apart, completely independent of each other, have arrived at the same answer to the fundamental question
How much water is needed to control confined structure fires?
One of the formulas is expressed in English units while the other is expressed in metric units. So what we must do is to transform the Royer Nelson formula into metric units so that we can compare it with the second formula in metric units.
The mathematics that follows may be tedious, but it is basically simple manipulation of an equation using one fundamental rule. Whatever you do to one side of an equation you must do to the other side. The same rule applies to fractions. We will use the conversion equations for converting from the English system to the metric system. There are two changes to be made, from gallons to liters and from cubic feet to liters. First let’s change from gallons to liters. One gallon equals 3.786 liters.
| Gpm x t = (Vol/200) |
| (3.785 x Gpm) x t = (3.785 x Vol)/200 |
The expression (3,785 x Gpm) changes to Lpm, so we will make that change. Next we will multiply the equation by 28.3 which is the conversion number for cubic feet to liters.
| 28.3 x Lpm x t = (3.785/200) x (Vol x 28.3) |
The expression (Vol x 28.3) changes volume from cubic feet to liters. We will use the symbol “Voll” to indicate that volume is now in liters.
| 28.3 x Lpm x t = (3.785/200) x Voll |
The next step is to divide both sides of the equation by 28.3
| (28,3/28.3) x Lpm x t = (3.785 x Voll)/(28.3 x 200)) |
Since n/n = 1 and 1 x n = n, this simplifies the left hand side of the equation. The numerical fraction on the right side is 3.785/5,660. What we want is to place the quotient in the denominator so that our equation will look like the original Royer Nelson formula. This is purely arithmetic, the manipulation of fractions which produces the following result.
- 3.785 ÷ 3.785
- 5,660 ÷ 3.785
And this produces the denominator that we want.
| Lpm x t = Voll/1,495 |
The number “1.495” may be rounded to the two places to give better accuracy for these calculations.
| Lpm x t = Voll/1,500 |
Volume is usually expressed in cubic meters. This final change is easy to make in the metric system. One cubic meter equals 1,000 liters, so dividing the numerator and denominator of the fraction (Voll / 1.500) by 1,000 produces the following equation with volume symbolized by Volm in cubic meters. Also please note that in the metric system “1.5” is written as “1,5” The commas and decimal points are interchanged between the English and metric systems. Perhaps you may have noticed this already in the metric equations previously written.
| Lpm x t = Volm/1,5 |
The second formula was published on the internet at HYPERLINK "http://www.firetactics.com" www.firetactics.com in 1999 by Paul Grimwood in an article “Compartment & Structural Firefighting, Water Flow Requirements”. The formula is
| Lpm = A x 2 |
The formula is in metric unites with Lpm equal to liters per minute, and “A” equals area of a compartment in square meters. It is easy enough to convert this formula to volume by multiplying by ceiling height In addition time is an essential element of any r.o.f. formula, so “t” must be added as well. Multiplying by 3 m (10 ft) gives the formula
| Lpm x t = ((3 x A) x 2)/3 |
(3 x A) equals volume in cubic meters symbolized by “Volm”. Simplify this equation by multiplying the numerator and denominator of the fraction by ½ gives the final form of the r.o.f. formula
| Lpm x t = Volm/1.5 |
This equation is, of course, identical to the Royer Nelson formula in metric units.
What is the significance of this finding? Both formulas were created independently of each other in different countries 36 years apart. Both formulas were the result of careful research. This convergence adds further proof to the validity of the critical r.o.f. formulas. It is safe to say that this formula is the only valid formula that the fire service will ever have to work with for confined structure fires.
