U p l a I Med Sci 79: 45-50, 1974 Estimation of the Maximal Work Rate Sustainable for 6 Minutes Using a Single-level Load or Stepwise Increasing Loads LARS-OLOF NORDESJO From the Military Medical Examination Centre ( M M U C ) and the Department of Clinical Physiology (Head: Prof. T . Sjostrand), Karolinska sjukhuset, Stockholm ABSTRACT Twenty-seven young men participated in four different types of maximal work tests: the Tornvall maximal ergometer test with a constant load and a work time of about 6 min, a maximal work test with two increases in load after 12 and 18 min work and a work time of about 21 min, a work test with increase in load every 6th minute until exhaustion, and a maximal work test on constant load during which maximal oxygen uptake was determined. A method based on the relationship between log load and log work time is proposed for estimation of physical work capacity expressed a s WmaX ~ min from work tests with increasing loads. Wm,, calculated in this manner differs very little from the results obtained from a work test with a constant load and a work time of about 6 min (the Tornvall test) and the coefficient of correlation and standard error of residuals are of the same magnitude (r = 0 . 9 5 4 . 9 7 ; se = 64- 88 kpm x min-') as those obtained from a test-retest of theTorn- vall test (r = 0.97; se = 59 kpm x min-I). The Tornvall test also shows a very strong relationship with the maximal oxygen uptake (r = 0.88). On the basis of earlier studies (1, 4) and his own in- vestigations Tornvall (8) assumed that a linear rela- tionship existed between the logarithms for maximal work time and load for work on a bicycle ergometer. This relationship may be expressed as follows: log T = u + P l o g N + e (1) where N = load, T = maximal work time at load N , tc and ,!? =constants, and e = a remainder term caused by disturbing factors. Tornvall tested a number of individuals (including 52 conscripts and 28 other young men) at different loads and calculated the mean of the individual esti- mates of ,!?. This was -4.959 for the conscript group and, with the aid of this value, Tornvall stated that one could estimate the highest load an individual can sustain for 6 min ( W,,, by letting him work to exhaustion at an arbitrarily selected load and insert- ing the values for T and N in the equation log T - log 6 log Wmax 6 rnin = 4.959 + log N In the case of work times of less than I min or more than 18 rnin a new test must be made at a more appropriate load, as it had not been confirmed whether the equation held good also for work of shorter or longer duration. Tornvall also stated that the estimate became considerably more reliable if the range for permissible work times was reduced to 1-12 min. As a new system for registration of conscripts into the Swedish armed forces was being investigated, it was suggested that the medical examination should include a work test ad modurn Tornvall. The primary idea was that, to simplify the examination procedure in the new system, all draftees should be tested at the same load (1 400 kpm x min-')l. A pilot study, how- ever, showed that about 25% could sustain this load for m x e than 12 rnin and about 9 % more than 18 min. In a discussion of the results of the pilot study the present author suggested that, by raising the load by 200 kpm x min-' after 12 min, the proportion of those exceeding the 18-min limit would be reduced and that, for those exceeding this limit, the test should not be interrupted but that the load should instead be raised by an additional 200 kpm x min-' every 6th minute. The first aim of the present study was t o test the Tornvall procedure and to compare the results ob- tained at a constant load and work time between 2 and 12 rnin with 1) a maximal work test in which the load is raised 1 kpmxmin-'=0.1634 watt; 1 watt=6.118 kpmxmin-l. Upsala J M e d Sci 79 46 Lars-Olof Nordesjo Table 1 . Physical characteristics and selected data on physical working capacity for the 27 subjects and 18- year-olds at registration (n = 1718) ~~ The subjects Boys of 18 Variable 2 S.D. Range X Age, years 22.37 22 18.7-27.0 Height, cm 180.6 6 . 9 169-192 177.2 Weight, kg 67.8 7.8 54.5-85.0 66.4 Heart volume, ml 734 98 520-910 673a Wmsxamin. k p m x 1 6 1 6 241 1 180-2002 1 4 5 1 min-' Maximal oxygen uptake 3.406 483 2.65-4.39 I x min-' ml x kg-l x min-' 50.4 6 . 4 37.5-63.4 Calculated from micro X-rays taken in a standing position. after 12 min by 200 kpm x min-' and after 18 min by an additional 200 kpm x min-' and the total work time is at least 18 min, 2 ) a graded maximal work test in which the load is raised by 300 kpm xmin-' every 6th minute until exhaustion. Another aim was to study the reliability of the original Tornvall test, at a constant load and with a work time between 2 and 12 min, and the relation of this test t o maximal oxygen uptake. MATERIAL The material consisted of 27 male university students. The subjects applied in response to an advertisement and re- L o o d , kpm , min-' f I I 300 k p m x min-1 N t - - _ I c T i m e . m i n 1 I I I 0 G 12 18 2 4 30 Fig. 1. Sequence of change in load. Nb=initial load work test type 6. N c = initial load work test type c. Upsala J M e d Sci 79 Ttme. rill" t Fig. 2. Recalculation and addition of work times in work test type b. See text. ceived a remuneration which covered their travel expenses a n d offered a moderate stimulus. Data of the 27 subjects will be seen in Table I, from which it appears that the subjects were somewhat older and very slightly taller and heavier than 18-year-old draftees and that their working capacity measured as W,,, min was con- siderably higher. METHODS Height was measured to within 1 cm and weight to the nearest 0.1 kg. Heart volume was calculated according to the formula proposed by Kjellberg et al. (3) from anterio-posterior and lateral roentgenograms, taken with the tube at right angles t o the table. T h e subject was placed in a supine position with cranially extended arms. ECG was recorded at rest with 1 1 leads on an Elema- Schonander Mingograf 4 2 or 34. CH2 - CH, were recorded during the first work test, CH, in the others. T h e tests were carried out on a n electrically braked ergo- meter-Elema-Schonander Model A M 368 (2). No changes were detected in the calibration when the ergometers were checked before, during and after the experiment. The length of the pedal lever was 17.5 cm. I n order that a work test should be judged as maximal, i t was required that the heart rate at end of work was at least 175 beats per rnin and that, on close supervision, the subject was deemed to be so exhausted as not t o be able t o continue t o work o r t o maintain the prescribed rate of revolutions (60 r.p.m.). In n o case was it necessary t o reject a test. During the test the subject was encouraged t o continue work until complete exhaustion. Even if the expected work time, which was unknown t o the subject, had been attained, the encour- agement continued with unchanged intensity. Estimation of maximal work capacity 47 Table 11. Heart rate at termination of work, total work time, and physical work capacity ( Wmax obtained from the various work tests Final heart rate, Work time, Wmax e min' beats x min-' min kpm x min-' Work test j . S.D. Range X S.D. Range 2 S.D. Range preliminary test 193.2 7.74 175-210 11.24 6.10 2.5-20.3 1603 256 1 174-2085 (type b) Type aia 190.5 7.84 175-200 6.54 1.64 4.4-10.7 I 6 1 6 241 1180-2002 Type b 195.7 8.01 185-218 22.06 1.49 19.2-25.1 1649 261 1186-2 114 Type 01; 190.7 7.66 1 7 6 2 0 4 5.84 1.00 4.1- 7.7 1 6 1 0 256 1 122-2074 Determination 191.3 7.66 182-208 16.26 1.19 14.5-19.7 of Vozmax Type 01: 190.4 7.56 176-200 5.79 1.05 4.1- 7.7 1607 270 1 122-2074 Type cb 192.2 6.81 185-208 24.72 3.67 19.8-31.3 1597 268 1073-2083 0 I = first series, 11 = second series. n-24. Four variants of work tests were used: (a) A work test ad modum Tornwall (at constant load), for which the result was calculated in accordance with equation (2). This test is called test a in the following. ( b ) A work test in which the load was raised by 200 kpm x min-' after 12 and again after 18 min (and, if necessary, additional increases by 200 kpm x min-' every 6th minute) as shown in Fig. I . This test is called test b in the following. From the result of this test Wm,, ~ min was estimated as follows. According t o equation (2) 12 rnin at load Nisequiv- alent (in respect of W,,,, to t i rnin at load N f 2 0 0 , where log ti = log 12 - 4.959 [log ( N + 200) -log N ] (3) T o t ; was added the time, t , (= 6 min), worked by the subject at load N + 200 and, analogously, the work time, t i , at load N + 4 0 0 was calculated which corresponded to ( t i + f,) rnin at load N + 200: log t i = log ( t i + t,) - 4.959 [log ( N + 400) - log ( N + ~ o o ) ] (4) To r i was added the time, t,, worked by the subject at load N+400. (If the load was raised three times, an additional recalculation and addition were made.) W,,, was ob- tained from the equation log (ti + t h ) - log 6 4.959 + l o g "+ ( h x 2OO)J (5) log wmax e min = where h = n u m b e r of increases of load. The manner of recalculation and addition of the work times is illustrated in Fig. 2. (c) A work test in which the load was initially 300 o r 600 kpm x min-' but was raised by 300 kpm x min-' every 6th minute as shown in Fig. 1. This test is called test c in the fol- lowing. The result was calculated analogously to that for test b: log ti = log 6 -4.953 [log ( N + 300) -log N] (6) log ri=log(t;+6)-4.959 [ l o g ( N + 6 0 0 ) - l o g ( N + 3 0 0 ) J (7) Further recalculations were made analogously t o equations (6) and (7) until W,, could be obtained from the equa- tion log (ti + t h ) - log 6 4.959 + l o g ( N + h x 300) (8) log Wmax e rnin = ( d ) A work test during which maximal oxygen uptake was determined. After a 10-min warm-up at 50% of the maximum load which the subject was calculated t o sustain for 6 minutes ( W m a x min) the load was raised to Wmax min- 50 kpm x min-'. After 3 minutes at the higher load a mouthpiece was inserted and, after an additional minute, the collection of ex- pired air (45-sec portions) in Douglas bags started. Duplicate analyses were made of the samples by the Haldane technique (precision 1/(Cd2),2n = 0.025 vol % 02) Volm,x was indicated as the highest value of oxygen uptake obtained for each subject. EXPERIMENTAL PROCEDURE At a preparatory visit the subject was given a general examina- tion comprising, inter alia, heart-lung radiogram, ECG and physical examination, and a work test of type b in which the starting load for all subjects was 1 400 kpm x min-'. I n a first series a work test of type a and a work test of Upsala J M e d Sci 79 48 Lars-Olof Nordesjo Table 111. Differences and relationships between the work tests Work test x1 x2 n (kpm x min-') (kpm x min-') r (kpm x min-I) Regression equation 4 - 2 . S.D.,. seb Typea; Type b 21 - 3 2 . g d 68.5 0.966 63.6 xI=O.892 x,+ 145 Type aI Type 011 21 6.3 62.0 0.971 59.0 x1=0.953 x,i- 145 Type aII Type c 24 10.0 86.0 0.948 87.7 x1 = 0.953 x2 + 85 Type a11 vo2max 21 0.881 118.0 x1 = 445.9 x2 + 81 27 0.881 0.23e x2=0.00174 x1+0.62 ' se= standard deviation of residuals. I =first series, I1 = second series. p < 0.05. 1 x min-'. type b were performed. On the basis of the results from the test at the preparatory visit the load in test a was so chosen that the subject was expected to be exhausted after 6 min, and the starting load in test b so that the subject would be ex- hausted after 21 min. (The loads were, however, rounded off t o the nearest 50 kpm x min-'.) T h e two tests were per- formed at one week's interval and in random order. I n a second series 2-4) months after the first, a work test of type a was again carried out at the load (rounded off t o the nearest 50 kpm x min-') for which the expected maximal work time was 6 min, and the work test in which maximal oxygen uptake was determined was performed. The tests were executed in random order and with at least 3 days' interval (3-14 days). In a third series, 2-55 days after the second, test c was carried out with starting load 300 (or 600) kpmxmin-l. Owing t o temporary illness, 3 subjects did not perform this test. Means and standard deviations for the remaining 24 subjects have been reported earlier (5). RESULTS Table I1 shows the mean, standard deviation and range for final pulse rate, actual work time and W,,, calculated from the various tests. In Table 111 the various estimates of Wma,6 are compared, and it will be seen that the differences in mean values are small. Only in one case is the dif- ference significant ( p < 0.05). The covariation between the different estimates of W,,, is very high. In all cases r is 0.95 or higher (see Table 111). For test a the test-retest reliability was high (r = Upsala J M e d Sci 79 0.97) although 3 months had elapsed between test and retest. The relation between maximal oxygen uptake and W,,, , calculated from test a , was high (r = 0.91, p <0.001), and with maximal oxygen uptake as de- pendent variable s, amounted to 0.234 1 x min-l (6.7 Yo). DISCUSSION The result of test b was significantly higher ( 3 3 kpm x min-') than that of test a. Correcting the result with regard to the mean difference, the stand- ard error1 in estimation of the result of test a from the result of test b was 68.5 kpm x min-', which may be compared with the standard error (62.0 kpm x min-I) obtained when the result was estimated from the result of the second series with test a. The com- parison is, however, not altogether fair as a con- siderably longer time ( 2 4 ) months) had elapsed between the two tests of type a than between the first test of type a and the type b test (one week). Probably the difference in standard error would have been greater if the time between the tests had been the same. The observation that the error tends t o be greater when the estimate is based on a test with duration about 22 min than on a test with duration about 64 min is in accordance with Tornvall's ob- I/""-"' 2(n - 1) Estimation of maximal work capacity 49 Table IV. Time in minutes to be added to the work time on the final b a d , when estimating W,,, from work test of type c *nation that the uncertainty is greater at work times exceeding 12 min. If the result is not corrected for the mean dif- ference, the standard error1 will be 76.2 kpm x min-1. The results can, of course, also be corrected accord- ing to the regression equation (Table 111), this leads to a standard error of the same order of magnitude (63.6 kpm x min-'). It cannot be asserted that in all contexts test b can be used instead of test a with a work time close t o 6 min. But for the examination of draftees the advantage of, if necessary, raising the load after 12 and I8 min instead of testing on another day and at a more suitable load should more than outweigh the slight uncertainty of the result. The procedure has implied that the proportion of draftees with work times longer than 18 min has been reduced from 9 % to below 3%. In the present study the work times in test b varied between 19.2 and 25.1 min, so that no major con- clusions can be drawn concerning the outcome of the test if carried out at a load which would have t o be raised more than twice. comparison of the results from tests c and a shows that W,,, (I can be estimated also from the for- mer. This is an advantage, as one can then obtain four ordinary measures of physical working capacity from a single work test, i.e., in addition t o Wmax6 also w170, HR,,, and the maximal oxygen uptake (kOz,,,,J estimated from the pulse rate. A more important advantage is that, in the same way as in testing with W,,,, one can follow the change of blood pressure, ECG etc. on gradual raising of the load, but, in contradistinction t o the normal practice in the W,,, test, by continuing to exhaustion or until the test must be stopped for reasons of safety, one ob- tains a more reliable estimate of the subject's maximal physical working capacity (or the highest load or pulse rate the subject can sustain without any un- toward reactions). The calculation of W,,, may seem com- plicated, but tables have been drawn up from which W,,, mfn can be directly read both for tests of type a and for tests of types b and c . It would require too much space t o reproduce these tables in this context, but Table IV may be of some assistance in conjunc- tion with test c. It shows the calculated time, t ; , t o be added to the time worked by the subject at the fi- - Final load, kpm x min-' Initial load (kpmxmin-')600 900 I 2 0 0 I500 1800 2 100 300 0.123 0.830 1.639 2.526 3.450 4.402 600 0.804 1.632 2.524 3.449 4.402 900 1.440 2.461 3.426 4.390 1 200 1.985 3.232 4.300 1 500 2.429 3.926 1800 2.795 nal load for different initial loads and for varying number of increases of load. It will be seen from the table that, when the load has been raised several times, the work a t the first loads has little signifi- cance for the estimate of W,,, (I If the subject stops after 3 min at 1 500 kpm x min-l, t ; + t h will be 5.526, 5.524, 5.461 or 4.985 min depending on whether the initial load was 300, 600, 900 o r 1200 kpm x min-', which implies that W,,, is 1475.5, 1475.4, 1471.5 and 1444.6 kpm xmin-' respectively. The test-retest reliability has also been tested in a field study of screening character. As the initial load in all cases was 1 400 kpm x min-' the test for those who were exhausted within 12 min was of type a, while the test for the remainder was of type b, since the load was raised by 200 kprn xmin-' a t 12 min and if necessary, also after 18 and 24 min. Even in this non-ideal situation the reliability was found t o be statisfactory ( r = 0.90, s, = 84.8 kpm x min-', n = 83). In another field study, likewise of screening character, a combination of tests a and b (initial load 1 400 kpm xmin-l in all cases in the same way as above) was compared with a work test of type c. With test c as independent variable the correlation was of the same order as in the laboratory study, whereas the standard error was rather higher ( r =0.90, s, = 105.5 kpm x min-l, n = 107). On this occasion the lactic acid level in the blood was determined a t the end of test a (or b) and the mean was found to be 12.2 mmol x 1-', S.D. 2.5 mmol x I-'. ACKNOWLEDGEMENTS This work was supported by a grant from the Delegation for Applied Medical Defence Research (Project No. 18: 090/68). Upsala J Med Sci 79 4 - 142854 50 Lars-Ofof Nordesjo REFERENCES I . Grosse-Lordemann, H. & Miiller, E. A.: Der Einfluss der Leistung und der Arbeitsgeschwindigkeit auf das Arbeitsmaximum und den Wirkungsgrad beim Rad- fahren. Arbeitsphysiol 9: 454-475, 1937. 2. Holmgren, A. & Mattsson, K . H.: A new ergometer with constant work load at varying pedalling rate. Scand J Clin Lab Invest 6: 137-140, 1954. 3 . Kjellberg, S. R., Lonroth, H. & Rudhe, U.: The effect of various factors o n the roentgenological determination of the cardiac volume. Acta Radio1 35: 413-427, 1951. 4. Miiller, E. A,: Die Abhangigkeit des Arbeitsmaximums von der Leistung bei verschiedenen Personen. Arbeits- physiol 10: 67-73, 1938. 5. Nordesjo, L.-0.: A comparison between the Tornvall maximal ergometer test, submaximal ergometer tests and maximal oxygen uptake, Forsvarsmedicin. In press, 1973. 6. Nordesjo, L.-0. & Schkle, R.: Validity of an ergometer cycle test and measures of isometric muscle strength when predicting some aspects of military performance. Forsvarsmedicin. In press, 1973. 7. Sjostrand, T.: Changes in respiratory organs of workmen a t ore smelting works. Acta Med Scand, Suppl. 196: 687, 1947. 8. Tornvall, G.: Assessment of physical capabilities. Acta Physiol Scand 58: Suppl. 201, 1963. 9. Wahlund, H.: Determination of physical working ca- pacity. Acta Med Scand 132: Suppl. 215, 1948. Received April 3 , 1973 Address for reprints: L.-0. Nordesjo Military Medical Examination Centre (MMUC) Fack S-104 01 Stockholm 60 Sweden Upsala J M e d Sci 79