Allometrically Scaling Firefighter Recruits

Allometric scaling aerobic capacity in firefighter fitness assessments.

Blake J. Surina
Exercise Science Center
1101 Regents Blvd.
Fircrest, WA 98466

May 18, 2009


Firefighting has long employed aerobic capacity evaluations in the creation and selection of appropriate fitness standards for entry-level firefighting candidates. These aerobic fitness standards are typically based on job specific tasks involved in firefighting, such as ladder evolution with a load, or ventilating a roof with an axe. One important consideration often neglected in the testing of firefighters is the effect of allometric scaling on the aerobic capacity requirements upon hiring.

Assessment of oxygen consumption as a measurement of aerobic capacity and cardio-respiratory fitness can be recorded in absolute terms, i.e. in liters per minute. Absolute measurement permits a decided advantage for larger subject’s as they possess larger lungs, larger muscles, increased blood volume, etc€¦ than similar proportioned, smaller subjects. To eliminate the impact of differing body mass when assessing oxygen consumption measurements, relative measurements, i.e. ml/kg*min-1, or METs, has become the industry standard for exercise physiology.

The acceptance of using a linear model in relative measurements of aerobic capacity, infers a person who is twice as big would need to perform twice the work of a smaller person at the same heart rate to obtain the same fitness level. Allometric scaling has proven that oxygen consumption measurements, in relative terms, should follow an exponential relationship closer to mass to the two-thirds power. Therefore, assessing relative aerobic capacity is specific to the body mass of the reference population from which the scoring and standards were created.

Creation of firefighter aerobic capacity standards for this study was created from a reference group of 21 firefighters (20 males, 1 female), with an average body mass of 86.9 kilos. Job specific aerobic tasks were given to the reference group of firefighters to derive minimum and maximum aerobic standards. Firefighter candidates were required to obtain a minimum aerobic standard of 10.4 METs to pass the aerobic phase of the physical assessment. These standards were then used in scoring pre-employment physical assessments for firefighting candidates seeking employment. (Erometrics,1991).

The purpose of this study is to illustrate the effects of allometric scaling on the selection of firefighter candidates with differing body mass than those from the reference population from which the fitness standards were created. A simple correction factor will be introduced that will allow a more equitable system of firefighter selection, using a Compensated Metabolic Equivalent of Task, termed a cMET. Incorporating an allometric model for assessing aerobic capacity will eliminate the inequalities of scoring candidates of differing body mass in the job selection process.


Twenty-three hundred and three firefighter, entry- level, physical assessments were performed at a local sports medicine laboratory. Firefighter candidate’s descriptive statistics are broken down by sex and shown in Table 1. The pilot, reference group of firefighters, used to create the aerobic fitness standards used in the scoring of the firefighter candidate’s are also included. Twenty-seven candidates from the original group of 2303 were selected for further evaluation to determine actual maximum volume of oxygen consumption, (Max VO2) measurements using indirect calorimetry.

Table 1: Descriptive Statistics of Firefighters and Firefighter Candidates


All candidates were weighed in their stocking feet, shorts and t-shirt to the nearest 0.1 kilogram, (Befour scale: Model PS 6600). Height was measured to the nearest 0.1 cm, using a wall-mounted stadiometer (Seca Accu-Height). Exercise heart rates (Polar Vantage XL) and workloads (Sensormedics Ergoline 800S) were recorded on the third of three stages using a submaximal bicycle protocol outlined by VonDoblen (1967). The regression equation by VonDoblem was used to estimate the candidates maximum aerobic capacity in MET’s (1 MET = 3.5 ml/kg*min-1). The resulting MET value was used in scoring the firefighting candidates in the job selection process.

It is well known in the scientific literature, that larger individuals are not as metabolically active per unit of mass as smaller individuals, Rubner (1883), Kleiber (1932), Hill (1950), Astrand (1977), McMahon & Bonner (1983), West (1997), Surina (2004), Seymour & White (2005). Therefore candidates that have a smaller body dimensions than the reference group would have an advantage in scoring whereas larger candidates would be handicapped. Direct comparisons of aerobic capacity measurements between the reference group of firefighters constructing the standards, and firefighter candidates being assessed can be made. By introducing a correction factor to relative oxygen consumption values (MET’s), inherent body mass differences between the reference group and the individual firefighter candidate can be addressed. The correction factor is as follows:

Candidates Weight ^(1/3)/Ref. Population Weight ^(1/3) = Correction Factor

In the simplest terms, the cube root of the candidates weight over the cube root of the reference population weight equals the correction factor. This correction factor is multiplied by the aerobic MET score obtained from a submaximal aerobic capacity assessment, and becomes the candidates allometrically scaled equivalent, a Compensated MET value, or cMET. For the purposes of this study, a comparison on the impact of allometric scaling and not scaling aerobic capacity scores (cMET versus MET), in the selection of firefighters for employment will be examined.

In addition, twenty-seven firefighters candidates from the 2303 assessments (26 males, 1 female), that attained cMET values between 9.2 and 10.8, were scheduled for Max VO2, aerobic capacity assessment, using indirect calorimetry, (Sensormedics Horizon, Yorba Linda CA). Protocol for testing used a bicycle ergometer (Sensormedics Ergoline 800s), and workloads were increased from 25 €“ 50 watts every 2 minutes until the subject could no longer continue. Subjects were allowed to sprint at the very end of the test, when they had reached a near maximum effort. Since the possibility of employment was enhanced on passing with a high Max VO2 score, motivation to achieve a maximum effort from the candidates was high. Max VO2 assessment times were typically between 9 and 15 minutes.

Using SPSS 13.0 software, statistical correlation coefficients will be made between the 27 candidate’s body weight and actual oxygen consumption, and to oxygen consumption estimates in MET and cMET values. The purpose is to determine if oxygen consumption measurements are truly independent of body mass for firefighter candidates when using allometrically scaled cMET values.


Of the 2303 aerobic assessments given, approximately 311 (13.5%) failed to obtain the minimum aerobic requirement for hiring of 10.4 METs Allometric scaling the firefighters results identified 127 assessments that were classified incorrectly (40.8%). Ninety-three candidates were incorrectly classified as false negatives, and thirty-four candidates were incorrectly classified as false positives. Of the eighteen female candidates that were incorrectly classified, all were found to be false positives. The pass/fail results of the candidates with and without allometric scaling are show in Table 2.

Table 2: Effect of Allometric Scaling in the Hiring of Firefighter Candidates

Twenty-seven candidates tested for actual oxygen consumption using respiratory gas analysis, found a significant correlation (r=.469) between body weight and oxygen consumption recorded in liters. This positive correlation showed that larger subjects had higher oxygen consumptions than smaller subjects performing the same tasks. Reporting oxygen consumption measurements in relative terms, a low correlation of r=.229, was shown that was not significant. By scaling the relative oxygen consumption scores from the respiratory gas analysis, the correlation coefficient was reduced to -.002, and showing no relationship to body mass in similarly conditioned firefighter candidates.

Estimated relative oxygen consumption MET values showed a significant negative correlation to body mass of r=-.689. The purpose of relative scoring has been purported to eliminate the effect of body weight on aerobic capacity measurements. This proved not to be the case. However, when the same data was allometrically scaled, oxygen consumption values (cMET) showed no relationship (r=-.019), between body weight and relative oxygen consumption scores in similarly conditioned firefighter candidates.

Table 3: Correlation of Subject Weight to Relative and Absolute Aerobic

Capacity Measurements


Firefighting is an occupation where that the lack of allometric scaling has had a profound impact on the selection of qualified candidates. Based on the currently accepted practice of recording relative oxygen consumption measurements, we will continue to favor smaller individuals and unfairly punishing larger individuals in aerobic capacity evaluations. As the jobs become more competitive and aerobic standards are increased, it will be increasingly difficult for larger candidates to meet standards and to receive appropriate scoring for aerobic capacity measurements. This is equally applicable to relative strength tests that are often used in firefighter assessments where a percentage of the candidates body weight is lifted a set amount of repetitions.

Per-Olof Astrand in his book Textbook of Work Physiology (1977) stated €œMaximal oxygen uptake, expressed as ml*min-1* kg-2/3, is not related to body weight and therefore can be used as a meaningful fitness index instead of the conventional method of expressing maximal oxygen uptake as ml*min-1*kg-1, which penalizes heavy individuals.€ Astrand was commenting on the original work of O.Vaage and L. Hermansen, showing the apparent relationship of body weight to maximal oxygen consumption in ml*min-1*kg-1, of r=-0.69. The same investigators noted that when using the units ml*min-1*kg2/3 there was no apparent relationship to body weight showing a correlation coefficient of r=-0.06.

Our study of 2303 firefighter candidates found nearly identical correlations between body weight and oxygen consumption in METs of r=-0.689. When allometrically scaled and recorded in cMETs the relationship between body weight and oxygen consumption was eliminated, r= -0.019. This was also noted in the twenty-seven firefighter candidates selected for the respiratory gas analysis. Despite the narrow range of estimated and actual aerobic capacity scores recorded by the candidates, the noted relationship between body weight and relative aerobic capacity measurements, were virtually eliminated through the use of allometric scaling, r=-0.002).

Fair and equitable aerobic capacity and strength standards for firefighters are possible, by adopting simple allometric scaling techniques. By adopting a system such as the Compensated MET (cMET) fire departments can eliminate a large percentage of inherent error in metabolic measurements that has been perpetuated over the last few decades. Continuing to accept the MET of 3.5 ml/kg*min-1 as the industry standard for everyone regardless of size, will sacrifice much of the ability for the science of exercise physiology to progress in the future.


Astrand, P.O., & Rodahl, D. (1977) Textbook of work physiology: Physiological bases of exercise. New York: McGraw-Hill.

Dobeln, W., Astrand, I. & Bergstrom, A. (1967) An analysis of age and other factors related to maximal oxygen uptake. Journal of Applied Physiology. 22(5), 934-938.

Hill, A.V. (1950) The dimensions of animals and their muscular dynamics. Science Progress. 38: 209-230.

Kleiber, M. (1932) Body size and metabolism. Hilgardia. 6, 315-353.

McMahon, T.A., & Bonner, J.T. (1983) On size and life. New York: W.H. Freeman.

Rubner, M. (1883) Ueber den Einfluss der Korpergroesse and Stoff- und Kraftwechsel. Z. Biol. Munich. 19, 535-562.

Surina, B.J., Method for adjusting metabolic related variables according to a subject’s body weight, United States Patent ID. US7344508, Issue Date: March 18, 2008.

White, C., & Seymour, R.S., (2005) Allometric scaling of mammalian metabolism. Journal of Experimental Biology 208, 1611-1619.

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