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Determination, measurement, 
and validation of maximal aerobic 
speed
Govindasamy Balasekaran *, Mun Keong Loh , Peggy Boey  & Yew Cheo Ng 
This study determined Maximal Aerobic Speed (MAS) at a speed that utilizes maximal aerobic and 
minimal anaerobic contributions. This method of determining MAS was compared between endurance 
(ET) and sprint (ST) trained athletes. Nineteen and 21 healthy participants were selected for the 
determination and validation of MAS respectively. All athletes completed five exercise sessions in 
the laboratory. Participants validating MAS also ran an all-out 5000 m at the track. Oxygen uptake 
at MAS was at 96.09 ± 2.51% maximal oxygen consumption ( ˙VO2max ). MAS had a significantly higher 
correlation with velocity at lactate threshold (vLT), critical speed, 5000 m, time-to-exhaustion 
velocity at delta 50 in addition to 5% velocity at ˙VO2max  (TlimυΔ50 + 5%v ˙VO2max ), and Vsub%95 (υΔ50 
or υΔ50 + 5%v ˙VO2max ) compared with v ˙VO2max , and predicted 5000 m speed  (R2 = 0.90, p < 0.001) 
and vLT  (R2 = 0.96, p < 0.001). ET athletes achieved significantly higher MAS (16.07 ± 1.58 km·h−1 
vs. 12.77 ± 0.81 km·h−1, p ≤ 0.001) and maximal aerobic energy  (EMAS) (52.87 ± 5.35 ml·kg−1·min−1 
vs. 46.42 ± 3.38 ml·kg−1·min−1, p = 0.005) and significantly shorter duration at MAS (ET: 
678.59 ± 165.44 s; ST: 840.28 ± 164.97 s, p = 0.039). ST athletes had significantly higher maximal speed 
(35.21 ± 1.90 km·h−1, p < 0.001) at a significantly longer distance (41.05 ± 3.14 m, p = 0.003) in the 50 m 
sprint run test. Significant differences were also observed in 50 m sprint performance (p < 0.001), and 
peak post-exercise blood lactate (p = 0.005). This study demonstrates that MAS is more accurate at 
a percentage of v ˙VO2max than at v ˙VO2max . The accurate calculation of MAS can be used to predict 
running performances with lower errors (Running Energy Reserve Index Paper).
The measurement of Maximal Aerobic Speed (MAS) is essential for determining aerobic and anaerobic perfor-
mances of various athletes. However, there is a lack of agreement on the definition and measurement of MAS in 
existing  literature1. Terms such as maximal velocity  (Vmax), velocity at maximal oxygen uptake  (v ˙VO2max ), peak 
running velocity, and maximal aerobic velocity have been used to represent MAS. Studies have predominantly 
considered v ˙VO2max as  MAS1,2. However, there is a high variability in the literature regarding the speeds and 
increments used to measure v ˙VO2max , which is reported to produce different results for the same  runner3. 
Studies on the relative importance of aerobic and anaerobic energy during running have suggested that time to 
exhaustion  (Tlim) at v ˙VO2max utilizes a higher amount of anaerobic energy and therefore selecting v ˙VO2max as 
MAS may not be  accurate4–6. Since MAS should utilize maximal aerobic energy  (EMAS) and minimal possible 
anaerobic energy contribution, MAS should be lower than v ˙VO2max at a precise speed with a corresponding 
lower blood lactate (BLa)  response1. In addition, there is a wide range of intergroup variation in maximal oxygen 
uptake ( ˙VO2max) between individuals, which vary according to the athletic background and gender of the  athlete7. 
Hence, there is currently no universal acceptance of a single standard of measure of MAS.
Exercising above critical speed (CS), which is close to the velocity of lactate threshold (vLT), leads to slow 
additional increases of oxygen uptake ( ˙VO2)8. Lactate threshold (LT) is usually detected at the point where 
BLa has a nonlinear increase during exercise as it reflects net lactate production that had exceeded lactate elimi-
nation. Such BLa concentrations are usually taken during graded incremental exercise tests that indicate lactate 
curves. Therefore, the shift in lactate curves indicate a change in aerobic capacity, also known as  LT9. This slow 
component of ˙VO2 becomes apparent at approximately 80–110 s from the start of maximal effort exercise, where 
a range of speeds is estimated as  EMAS
10. One of the proposed intensities at which  EMAS can be determined is 
known as velocity of delta 50 (υΔ50), the median of v ˙VO2max and  vLT11. Measurements for vLT, v ˙VO2max , and 
υΔ50 of 8 highly trained long distance runners found υΔ50 to be at 91% of ˙VO2max ( ˙VO2max = 59.8 ml·kg−1·min−1, 
v ˙VO2max = 18.5 km·h−1, vLT = 15.2 km·h−1, υΔ50 = 16.9 km·h−1)12. However, this speed did not seem to elicit  EMAS 
OPEN
Human Bioenergetics Laboratory, Physical Education and Sports Science, National Institute of Education, Nanyang 
Technological University, 1 Nanyang Walk, Singapore 637616, Singapore. *email: govindasamy.b@nie.edu.sg
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in trained  athletes8. Hence, a hypothetical minimum intensity of υΔ50 + 5%v ˙VO2max will be used in this study 
for participants who did not achieve  EMAS at υΔ50.
Anaerobic energy utilization is estimated as the time spent at ˙VO2max during  Tlimv ˙VO2max . This is based on 
the assumption that anaerobic energy stores will be completely depleted during  Tlim at intensities above  CS13. 
This has been demonstrated in previous studies assuming that maximal anaerobic energy  (EMAnS) was consumed 
during 800–5000  m14 as well as 1500–10,000  m15 runs. It is necessary to select the intensity at which the con-
sumed anaerobic energy is a representative of the anaerobic energy used at any run with an aerobic speed reserve 
(AeSR), where AeSR represents the difference between v ˙VO2max and  CS16. MAS lies at the extreme of the range 
between CS and v ˙VO2max . During  Tlimv ˙VO2max , the athlete attains  EMAS and uses  EMAnS with minimal aerobic 
contribution.  Tlim ˙VO2max determined at other intensities within this range may consume comparatively higher 
percentage of ˙VO2 and thus overestimate the anaerobic energy. Hence,  Tlim ˙VO2maxv ˙VO2max as anaerobic energy 
seems logical to measure duration at MAS  (MASdur) and MAS.
To determine MAS and  MASdur, anaerobic energy consumption at MAS has to be minimized without com-
promising its criteria.  MASdur can be calculated by subtracting anaerobic energy duration from ˙VO2max till 
exhaustion at Vsub%95  (TlimVsub%95). This method was based on the negative linear relationship between 
anaerobic and aerobic energy contribution during physical activity, as anaerobic energy contribution decreases 
with increasing exercise  duration17. Therefore, subtracting anaerobic energy duration from  TlimVsub%95 may 
provide an accurate determination of  MASdur.
The objectives of this study aimed to (1) determine MAS at a speed that utilizes maximal aerobic and minimal 
anaerobic contributions, where MAS should fulfill four criteria (a) MAS should be lower than v ˙VO2max, (b) maxi-
mal aerobic energy utilization is elicited during  Tlim test, (c) MAS should occur at a specific percentage fraction of 
v ˙VO2max , and (d) estimated anaerobic energy contribution at  TlimMAS should be lower than that at  Tlimv ˙VO2max . 
(2) To assess whether MAS can accurately differentiate between athletes of different training orientations (endur-
ance or sprint trained) and if there was an association between  MASdur  and aerobic performance variables of run 
distance and best performance times. It was hypothesized that the MAS of endurance-trained athletes would be 
higher than that of sprint-trained athletes, and that MAS measured would significantly correlate with 5000 m 
run performance and aerobic performances variables. This study has been separated into two parts. The first part 
of this study, which this paper is based on, utilizes a new framework of calculating MAS. This validated MAS 
was confirmed with the prediction of running performances in a follow-up paper that examined the Running 
Energy Reserve Index (RERI)18.
Methods
Participants. 
Forty participants volunteered for the study. Among the 40 athletes, 19 healthy participants 
(age: 29.74 ± 8.31 years; height: 171.86 ± 7.65 cm; body mass index (BMI): 22.01 ± 2.12 kg·m−2; body fat percent-
age (BF%): 12.96 ± 3.10%)) were selected to validate the theoretical framework criteria of MAS. The remain-
ing participants consisted of 9 sprint-trained athletes (age: 26.89 ± 9.39 years; height: 174.16 ± 5.69 cm; BMI: 
23.09 ± 2.07  kg·m−2; BF%: 10.59 ± 2.55%) and 12 endurance-trained athletes (age: 31.67 ± 7.24  years; height: 
173.67 ± 7.59 cm; BMI: 21.34 ± 1.27 kg·m−2; BF%: 12.74 ± 2.38%) (Table 1). These 21 athletes were selected to 
determine whether there were significant differences between the MAS of sprint-trained and endurance-trained 
athletes, and the relation of MAS with aerobic performances and variables.
Participants were considered trained if they were engaged in training for at least four sessions of 60 min per 
week in their chosen activities for the last 12 months. Among the endurance-trained athletes, 4 were triathletes 
Table 1.  Descriptive characteristics endurance-trained and sprint-trained athletes. Values are in means ± SD. 
BMI Body mass index, LBM Lean body mass, FFM Fat free mass, BMD Bone mineral density, BMC Bone 
mineral content, BLa Blood lactate. *p ≤ 0.05, **p ≤ 0.01: Indicates significant difference between endurance-
trained and sprint-trained athletes. † The data of two participants aged 14.5 ± 0.5 years were not included due 
to differences between age of these two participants and the total cohort and its effect on body  composition19 
(Boileau and Horswill  200320).
Variables
Endurance-trained
Sprint-trained
N
12
9
Age (years)
31.67 ± 7.24
26.89 ± 9.39
Height (cm)
173.67 ± 7.59
174.16 ± 5.69
BMI (kg·m−2)
21.34 ± 1.27
23.09 ± 2.07*
Fat percentage (%)
12.74 ± 2.38
10.59 ± 2.55
Hematocrit (%)
43.51 ± 2.30
45.59 ± 1.34*
Haemoglobin (g·dl−1)
14.79 ± 0.78
15.50 ± 0.46*
Plasma volume (%)
56.49 ± 2.30
54.41 ± 1.34*
LBM (kg)†
53.13 ± 5.50
58.76 ± 4.43*
FFM (kg)†
55.68 ± 5.80
61.69 ± 4.65*
BMD (g·cm−2)†
1.19 ± 0.07
1.28 ± 0.10*
BMC (kg)†
2.61 ± 0.23
2.93 ± 0.29*
Rest BLa (mmol·L−1)
0.71 ± 0.13
0.83 ± 0.16
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and had completed the ironman distance race (3.86 km swim, 180.25 km bike, and 42.195 km run) several times. 
The other 6 participants were training for half and full marathon, and the remaining 2 were 10 km runners. 
The sprint-trained athletes were specialized in soccer and 100–400 m sprint events, and they were still actively 
competing in their respective events. Participants who had any history of musculoskeletal injuries in the past 
6 months, smokers and medical history were exempted from this study. All participants were informed of the 
risk and benefits of the study and gave their informed consent to participate. This study was approved by the 
Ethical Review Board of the Research and Graduate Studies Committee of Physical Education & Sports Science, 
National Institute of Education, Nanyang Technological University, Singapore. All methods were performed in 
accordance with the relevant guidelines, regulations and STROBE checklist.
Experimental design. 
The experimental design and procedures in this study were derived and modified 
from Bundle et al.21. A within cross-sectional design was utilized in each investigation, where each partici-
pant underwent a series of exercise tests to determine MAS accurately. Participants completed exercise sessions 
which included (1) aerobic metabolic measurement utilizing Astrand modified running (AMRMAX) continu-
ous incremental maximal treadmill protocol, (2) submaximal discontinuous treadmill run (SUBMAX) protocol, 
(3)  Tlim at v ˙VO2max , (4) Test of  Tlim at Vsub%95, and (5) speed and duration test protocols. To assess the validity 
of MAS, participants also ran an all-out 5000 m on the track. Participants were instructed to avoid strenuous 
activities, alcohol, and caffeine 24 h before testing.
All laboratory sessions were conducted at the Human Bioenergetics Laboratory in the Physical Education and 
Sports Science department of the National Institute of Education, Nanyang Technological University, Singapore, 
while the 5000 m track test was performed on the 400 m track located at the Sports and Recreation Centre of 
Nanyang Technological University, Singapore.
Pretest preparations. 
Prior to the tests where cardiorespiratory and aerobic metabolic parameters were 
measured, the flow meter, sampling line and gas calibrations of ParvoMedics TrueOne 2400 (ParvoMedics Inc, 
UT, USA) were performed according to the procedures explained in the instruction manual (Operator’s guide, 
Version 4.3, ParvoMedics Inc, UT, USA 2008). Heart rate (HR) transmitters were strapped onto the participants’ 
chest, and participants were required to put on the head cap, mouthpiece of a two-way non-rebreathing valve. 
A nose-clip was used to ensure all expired air are analyzed. In addition, participants were strapped in an upper 
body safety harness to prevent falling while running on the treadmill belt at various speeds. The harness did not 
assist or impede the participants during the tests.
Experimental tests and measurements. 
Participants were instructed to stride the belt of the treadmill 
before the tests, and to hold the handrail of the treadmill or give a ‘thumbs down’ signal to stop the test due to 
exhaustion or discomfort. All the laboratory tests were performed on a motorized treadmill (H-P Cosmos, UK). 
The gradient was set at 1% for all treadmill running protocols except for ˙VO2max  protocol22. Participants were 
encouraged to deliver their maximum effort during tests.
Before performing the ˙VO2max test, height and weight of participants were recorded, and a Dual-Energy 
X-ray absorptiometry (DEXA, QDR 4500W, Hologic Inc, Waltham, USA) scan was performed to determine 
body composition. Subsequently, capillary blood sample was collected via the finger prick technique to measure 
resting BLa.
Astrand modified running continuous incremental maximal treadmill (AMRMAX) protocol. The AMRMAX 
protocol was employed to determine ˙VO2max of participants. The test began with an initial speed of 8–12 km·h−1 
with 0% gradient. After 3 min of running, the gradient was increased by 2.5% at 2 min stages until volitional 
exhaustion. Thereafter, post-exercise capillary whole blood samples were taken from the finger at every minute 
for 5 min. BLa was analyzed via YSI 2300 STAT Plus (2300 D, YSI Incorporated, USA) to measure peak post-
exercise BLa. The expired breath-by-breath gas concentrations were analyzed using ParvoMedics TrueOne 2400 
(ParvoMedics, Inc, USA) and averaged at every 15 s. HR was measured via a Polar HR transmitter (Polar Electro, 
Singapore) which sends its signals to the receiver of ParvoMedics TrueOne 2400 metabolic system (ParvoMed-
ics, Inc, USA).
˙VO2max was determined when participants satisfied three of the following five  criteria23: (1) Plateau of ˙VO2 
change in ˙VO2 ≤ 2.1 ml·kg−1·min−1 in spite of increasing treadmill gradient, (2) Respiratory exchange ratio (RER) 
at ˙VO2max ≥ 1.1, (3) BLa > 8 mmol·L−1, (4) HR ≥ 90% of the age predicted maximal HR  (HRmax), and (5) volitional 
 exhaustion9.
Submaximal discontinuous treadmill (SUBMAX) protocol. Participants performed a series of six to nine dis-
continuous submaximal treadmill runs. Initial speed was set at approximately 40–60% ˙VO2max with increments 
of 4–5% ˙VO2max at every stage depending on the ability of the participant. All running speeds were within the 
range of 40–90% ˙VO2max . Running sessions were fixed at 4  min23,24, with 2–4 min recovery between sessions. 
Capillary blood samples were obtained with the finger prick technique and were collected immediately after each 
submaximal running session. Steady state cardiorespiratory and aerobic metabolic measures were recorded at 
every 15 s during the 3rd and 4th minute of each treadmill running session.
vLT was then determined using a log–log plot  method25,26. The linear relation between run speeds and cor-
responding ˙VO2 were determined using a linear regression  analysis21,27,26. Linear relation determined through 
SUBMAX protocol was extrapolated to ˙VO2max , and this velocity at ˙VO2max was termed as v ˙VO2max26. The 
average of vLT and v ˙VO2max was calculated to determine υΔ50.
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Oxygen Consumption till Exhaustion ( ˙VO2max till exhaustion  (Tlim)) tests. Tlim tests were conducted at 100% 
v ˙VO2max  (Tlimv ˙VO2max ) and υΔ50. However, it was found that the participants could not reach ˙VO2max at υΔ50. 
Hence, 5%v ˙VO2max was added to υΔ50 for all participants to achieve maximal aerobic energy during the  Tlim 
test (υΔ50 ± 5%v ˙VO2max ). The speed at which  EMAS was attained during  Tlim at υΔ50 and υΔ50 ± 5%v ˙VO2max 
was termed Vsub%95. Achieving ≥ 95% ˙VO2max was selected as the primary criterion to measure time to attain 
˙VO2max (TA ˙VO2max ) during  Tlimv ˙VO2max and  TlimVsub%9527,19.
Participants performed a warm up protocol of 8–15 min at 60% ˙VO2max followed by a rest interval of 
5–10 min. During each of the  Tlim test, participants ran at a fixed speed for as long as possible until volitional 
exhaustion. Breath-by-breath cardiorespiratory and aerobic metabolic measures were recorded during each run. 
BLa samples were collected after warm up and at each minute of the first five minutes after individual  Tlim run 
to determine peak post-exercise BLa.
Breath-by-breath ˙VO2 responses recorded at  Tlimv ˙VO2max were interpolated per second and the time was 
aligned to the start of the run with an average at every five seconds via a moving average filter. Thereafter, the 
data was fitted to a positive exponential nonlinear regression by means of weighted least square method using 
SigmaPlot software (windows version 11.0.0.77, Germany) (Eq. 1). This equation was fitted to the data collected 
from  Tlim tests and TA ˙VO2max and  Tlim ˙VO2maxconverted were computed (Eqs. 2 and 3).
where ˙VO2baseline is the ˙VO2 before starting the  Tlim run, A is the amplitude of ˙VO2 ( ˙VO2max– ˙VO2baseline) for I, and 
II components, δ is the time delay before onset of each exponential component and τ is the time constant for 
each component of ˙VO2
28.
Speed and duration curve protocol. After pretest preparations, orientation trials were conducted by allowing 
participants to step onto the treadmill at fast speeds. Following a 5–10min recovery, the treadmill was set at a 
preselected speed. Participants then stepped on the moving treadmill with the use of the handrail and started 
unassisted running within 4–7 steps. They were instructed to run until volitional exhaustion, and both duration 
and run speeds at exhaustion were recorded. Full recovery was given between the trials, and they were allowed 
to discontinue the test if they were unable to perform at their best. A minimum of two to three trials were per-
formed at different speeds ranged from 110% v ˙VO2max to 140% v ˙VO2max. Participants were only allowed to per-
form the next trial if: (1) recovery HR was equal to or more than 120 beats·min−1 approximately, (2) participant 
gave consent for performing the test to the best of their abilities, and (3) duration of recovery was based on the 
principle of work to rest ratio.
Speeds in the range of 90–140% v ˙VO2max and their corresponding durations calculated during the different 
 Tlim sessions and speed-duration curve protocol were data fitted to determine hyperbolic relation (Fig. 1). MAS 
was then determined using Eq. 4.
(1)
˙VO2(t) = ˙VO2 baseline + A0 ×

1 − e
−

t
τ0

+ A1 ×

1 − e
−
 t−δ1
τ1

(2)
Tlim ˙VO2 maxv ˙VO2 max = Tlimv ˙VO2 max−TA ˙VO2 maxv ˙VO2 max
(3)
Tlim ˙VO2 max converted(s) =

Tlim ˙VO2 maxv ˙VO2 max × v ˙VO2 max

Vsub%95
Figure 1.  Hyperbolic relationship between speed and duration.
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where CS = critical speed; ADC = anaerobic distance capacity;  MASdur = duration at MAS; and B = constant.
A backward validation by predicting run performances was performed whereby  MASdur was calculated by 
adding the time representing anaerobic  energy18. Since there is a negative relationship between aerobic and 
anaerobic energy, aerobic energy was taken to be the negative of anaerobic energy. The following equation was 
employed for the calculation of  MASdur (Eq. 5):
The linear relation between speed and ˙VO2 (measured through the SUBMAX protocol) was extrapolated to 
MAS and the extrapolated ˙VO2 at MAS was considered as  EMAS
21.
50 m sprint run test. Participants performed a general 10–15 min warm up run at a comfortable pace fol-
lowed by dynamic stretching exercises. Following the warm up, participants performed strides of 20–40 m with 
3–5 min recovery between strides.
The 50 m sprint run was performed with a standing start position at the start line. At the start command, 
the athlete accelerated and covered the distance of 50 m in the least possible time. The speed and time at the 
stipulated distance intervals within 50 m were automatically recorded by the five timing gates placed within 
34–50 m for sprinters and middle distance runners and within 30–46 m for endurance athletes. A minimum of 
two trials were performed, with a 15–20 min rest interval in between the trials, and the best performance was 
recorded to the nearest 0.01 s.
5000 m test. Orientation trials were performed 1 week before testing to familiarize participants with the pace 
of their run to elicit the best effort in testing. Prior to the actual run, participants warmed up for 10–15 min at a 
comfortable pace followed by stretching exercises. A rest period of 3–5 min after the warm up was given before 
starting the test. Participants were encouraged to run at their targeted best effort based on their fitness level and 
ran the whole distance at their own self-regulated pace. The time taken to cover each run was recorded to the 
nearest 0.01 s.
Statistical analysis. 
Statistical analyses and data fitting procedures were performed using Statistical Pack-
age for Social Sciences (SPSS) version 17.0 and SigmaPlot software (version 11.0, Systat software, Inc., 2008, Ger-
many) respectively. Using a power of 0.80 and α level of 0.05 with an effect size of > 1.1, it was determined that 
a minimum of 10 participants were  required29. Linear regression was employed to calculate vLT, v ˙VO2max, and 
 EMAS. One-way ANOVA was utilized to measure any significant differences between BLa measured during the 
different  Tlim tests and BLa measured at ˙VO2max (BLa ˙VO2 max) . The Wilcoxon rank test (non-parametric paired 
t-test) and correlation technique were employed to significantly validate the criteria of MAS, and independent 
t-tests were employed to compare anthropometrical and body composition measures, cardiorespiratory and 
aerobic metabolic measures, and MAS between endurance-trained and sprint-trained athletes. Lastly, coeffi-
cient of correlation technique (very strong correlation: 0.9–1.0, strong correlation: 0.7–0.9, moderate correla-
tion: 0.5–0.7) was used to assess the relationship between MAS and aerobic parameters. Statistical significance 
was set at p ≤ 0.05 for this study.
Results
As shown in Table 2, anthropometrical, body composition, and hematological measures were significantly higher 
among sprint-trained athletes compared to endurance-trained athletes. However, the proportion of plasma 
volume was significantly higher among endurance-trained athletes. Figure 2 determined the steady state of the 
participants during the SUBMAX protocol calculated by the submaximal efficiency equation.
(4)
Speed

m · s−1
= CS +

ADC
B + MASdur

(5)
MASdur = TlimVsub%95−

−Tlim ˙VO2 max converted

Table 2.  Astrand Modified Running Protocol (AMRMAX) results in endurance-trained and sprint-trained 
athletes. Values are in means ± SD. ˙VO2max Maximal oxygen uptake, RERmax Respiratory exchange ratio at ˙VO
2max, HR ˙VO2max Heart rate at ˙VO2max, %HRmax Percentage of maximal heart rate, BLa ˙VO2max Blood lactate at 
˙VO2max. *p < 0.05, **p < 0.01: Indicates significant difference between endurance-trained and sprint-trained 
athletes. a Only 8 sprint trained participants were analyzed due to technical difficulties.
Variables
Endurance-trained
Sprint-trained
N
12
9
˙VO2max (ml·kg −1·min−1)
57.62 ± 5.40
51.12 ± 3.59**
RERmax
1.16 ± 0.03
1.12 ± 0.03a **
HR ˙VO2max (beats·min-1)
181.71 ± 14.31
185.06 ± 5.81
%HRmax at ˙VO2max
96.45 ± 6.02
95.89 ± 5.96
BLa ˙VO2max (mmol·L−1)
8.26 ± 1.72
8.17 ± 1.63
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MASdur calculation. 
MASdur was calculated by subtracting  Tlim ˙VO2maxconverted from  TlimVsub%95. This 
however resulted in MAS being higher than Vsub%95, which elicited higher anaerobic energy and thus failed to 
fulfil the MAS criteria. Figure 3 shows an example of a participant whose  Tlim ˙VO2maxconverted and  TlimVsub%95 
were at 159 s and 533 s respectively. Subtracting these two would have resulted in a corresponding speed at  MASdur 
of 16.9 km·h−1 on the speed-duration graph ((306 s = 5 min 6 s (16.9 km·h-1) → converted to  Tlimconverted = 159 s 
(using Eq. 3).  TlimVsub95 = 533 s—(−  Tlimconverted) 159 s = 692 s  (MASdur) (using Eq. 5), 692 s = 11 min 32 s)). This 
translated to 97.1%v ˙VO2max, which was close to v ˙VO2max at which  EMAnS was determined.
Using the same participant in Fig. 3, adding  Tlim ˙VO2maxconverted and  TlimVsub%95 together resulted in a cor-
responding  MASdur speed at 16.1 km·h−1, which was at 92.5%v ˙VO2max . It seemed that  Tlim ˙VO2maxconverted and 
 TlimVsub%95 fulfilled the criteria of achieving MAS. This suggest that accurate calculation of MAS will result in 
lower error of prediction of run performances with an average of 2.39 ± 2.04%  (R2 = 0.99,  nT (number of running 
trials) = 252)) for all athletes, with treadmill trials to within an average of 2.26 ± 1.89%  (R2 = 0.99,  nT = 203) and 
track trials to within an average of 2.95 ± 2.51%  (R2 = 0.99,  nT = 49)18.
Validation of MAS. 
The mean MAS was 14.50 ± 1.82  km·h−1. There was no significant difference 
between ˙VO2 at MAS (96.09 ± 2.51% ˙VO2max) and ˙VO2 at 95% ˙VO2max among all athletes ( ˙VO2 at MAS: 
Figure 2.  Determination of the submaximal efficiency equation between ˙VO2 and corresponding run speeds.
Figure 3.  Calculation of duration at MAS. (A) indicates the duration of MAS with anaerobic and aerobic 
energy. (B) indicates the calculation of MAS based on duration of  TlimVsub%95 and  Tlim ˙VO2maxconverted at 
 Tlimv ˙VO2max.
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50.18 ± 5.19  ml·kg−1·min−1 vs. ˙VȮ2 at 95% ˙VO2max: 50.69 ± 4.69  ml·kg−1·min−1, p = 0.134). In addition, mean 
BLa at MAS  (BLaMAS) (7.80 ± 1.52 mmol·L−1) was significantly lower than corresponding values at v ˙VO2max 
(9.11 ± 2.50 mmol·L−1; p = 0.009) and ˙VO2max (8.60 ± 1.62 mmol·L−1; p = 0.037). While  BLaMAS was not signifi-
cantly lower than BLa at Vsub%95  (BLaVsub%95) (8.01 ± 1.39 mmol·L−1, p = 0.174). RER, ventilatory threshold and 
HR at MAS were 1.05 ± 0.03, 2.19 ± 0.51 L·min−1 and 176.62 ± 26.72 beats·min−1 respectively.
MAS between endurance-trained and sprint-trained athletes. 
Endurance-trained athletes had sig-
nificantly higher mean ˙VO2max (p = 0.004) and RER at ˙VO2max  (RERmax) (p = 0.007) (Table 2). vLT (p < 0.001), BLa 
at LT  (BLaLT) (p < 0.001), ˙VO2 at LT ( ˙VO2LT) (p = 0.013) were significantly higher among ET athletes, while no 
significant differences were observed between both cohorts for HR at LT  (HRLT) (p = 0.467) and percentage of 
 HRmax (%HRmax) (p = 0.968) (Table 3). In addition, measured υΔ50 (p < 0.001) and υΔ50 + 5%v ˙VO2max (p < 0.001) 
were also significantly higher in endurance-trained athletes compared to sprint-trained athletes (Table 4).
All athletes attained ≥  95% ˙VO2max to calculate TA ˙VO2max at  Tlimv ˙VO2max and  TlimVsub%95 (Table 5). v ˙VO2max 
and Vsub%95 were significantly higher among endurance-trained athletes (p ≤ 0.001). However, sprint-trained 
athletes ran at these speeds for longer duration and hence  Tlim was significantly different compared to ET athletes 
(p = 0.030). No significant differences were determined between both cohorts for TA ˙VO2max  Tlim ˙VO2max, and 
BLa at  Tlimv ˙VO2max (p = 0.164) and  TlimVsub%95 (p = 0.264) (Table 5). Similar results were also calculated for 
 Tlim ˙VO2maxconverted (sprint-trained: 167.98 ± 52.28 s; endurance-trained: 125.75 ± 76.28 s, p = 0.171).
Mean CS (endurance-trained: 14.95 ± 1.40 km·h−1; sprint-trained: 11.52 ± 0.80 km·h−1, p < 0.001) was signifi-
cantly higher while ADC (endurance-trained: 221.60 ± 57.74 m; sprint-trained: 313.43 ± 139.74 m, p < 0.05) was 
significantly lower in endurance-trained athletes compared to strength-trained athletes. MAS range was between 
15.37 ± 1.57 km·h−1 (~ υΔ50) and 16.25 ± 1.64 km·h−1 (~ υΔ50 + 5%v ˙VO2max) among endurance-trained athletes 
and between 12.42 ± 0.81 km·h−1 (~ υΔ50) and 13.12 ± 0.85 km·h−1 (~ υΔ50 + 5%v ˙VO2max) among sprint-trained 
athletes.
Furthermore, endurance-trained athletes achieved significantly higher MAS (endurance-trained: 
16.07 ± 1.58 km·h−1; sprint-trained: 12.77 ± 0.81 km·h−1, p ≤ 0.001; 95% CI [2.091, 4.515]) and  EMAS (endurance-
trained: 52.87 ± 5.35 ml·kg−1·min−1; sprint-trained: 46.42 ± 3.38 ml·kg−1·min−1, p = 0.005; 95% CI [2.182, 10.716]) 
Table 3.  Submaximal discontinuous treadmill run (SUBMAX) test results in endurance-trained and sprint-
trained athletes. Values are in means ± SD. vLT velocity at lactate threshold, BLaLT Blood lactate at LT, ˙VO
2LT Oxygen uptake at LT, HRLT Heart rate at LT, %HRmax  Percentage of maximal heart rate; υΔ50 median of 
v ˙VO2max and vLT, υΔ50 or υΔ50 + 5%v˙VO2max mean speed of v ˙VO2max and vLT or mean speed of v ˙VO2max and 
vLT plus 5%v ˙VO2max. *p < 0.05, **p < 0.01, ***p < 0.001: Indicates significant difference between endurance-
trained and sprint-trained athletes.
Variables
Endurance-trained
Sprint-trained
N
12
9
vLT (km·h−1)
13.37 ± 1.58
10.48 ± 0.83***
BLaLT (mmol·L−1)
1.59 ± 0.59
2.60 ± 0.49***
˙VO2LT (ml·kg−1·min−1)
43.63 ± 4.15
38.76 ± 3.92*
HRLT (beats·min-1)
157.83 ± 15.42
161.96 ± 7.14
HRLT (%HRmax)
83.73 ± 6.60
83.83 ± 4.20
υΔ50 (km·h−1)
15.37 ± 1.57
12.42 ± 0.81***
υΔ50 + 5%v ˙VO2max (km·h−1)
16.25 ± 1.64
13.12 ± 0.85***
Table 4.  Oxygen kinetics and blood lactate at v ˙VO2max and Vsub%95 among endurance-trained and sprint-
trained athletes. Values are presented as means ± SD. v˙VO2max Velocity at ˙VO2max, Vsub%95 speed at υΔ50 
or υΔ50 + 5%v ˙VO2max at which maximal aerobic energy was obtained, Tlim ˙VO2 till exhaustion, TA˙VO2max 
Time to achieve 95%˙VO2max, Tlim ˙VO2max time spent at ˙VO2max, BLa Blood lactate. a Only 11 participants were 
analyzed due to technical difficulties. *p < 0.05, **p < 0.01, ***p < 0.001: Indicates significant difference between 
endurance-trained and sprint-trained athletes at  Tlimv ˙VO2max and  TlimVsub%95.
Variables
Endurance-
trainedv ˙VO2max
Sprint-
trainedv ˙VO2max
Endurance-trainedVsub%95
Sprint-
trainedVsub%95
Speed (km·h−1)
17.38 ± 1.62
14.33 ± 1.11***
16.25 ± 1.64
13.05 ± 0.82***
Tlim (s)
300.02 ± 67.43
358.50 ± 36.70*
552.84 ± 105.50
672.29 ± 120.98*
TA ˙VO2max (s)
182.61 ± 34.57
206.07 ± 39.85
356.89 ± 67.59a
367.31 ± 120.52
Tlim ˙VO2max (s)
117.41 ± 71.47
152.43 ± 45.17
215.77 ± 127.80a
304.98 ± 114.18
Tlim ˙VO2maxconverted (s)
125.75 ± 76.28
167.98 ± 52.28*
–
–
BLa (mmol·L-1)
8.96 ± 1.87
7.96 ± 1.68
7.97 ± 1.59
7.27 ± 1.25
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at significantly shorter  MASdur (endurance-trained: 678.59 ± 165.44 s; sprint-trained: 840.28 ± 164.97 s, p = 0.039; 
95% CI [− 314.190, − 9.177]) compared to sprint-trained athletes.
MAS was also significantly correlated to ˙VO2max (r = 0.78, p < 0.001), v ˙VO2max (r = 0.98, p < 0.001). In addition, 
MAS had comparatively higher correlations with vLT (MAS: r = 0.97, p ≤ 0.001; v ˙VO2max: r = 0.91, p < 0.01), CS 
(MAS: r = 0.99; v ˙VO2max: r = 0.93), 5000 m (MAS: r = − 0.95, p < 0.001; v ˙VO2max: r = − 0.92),  TlimυΔ50 + 5%v ˙VO
2max (MAS: r = − 0.71, p < 0.05; v ˙VO2max: r = − 0.62) and Vsub%95 (MAS: r = 0.997, p < 0.001; v ˙VO2max: r = 0.98, 
p < 0.01) compared to v ˙VO2max. MAS predicted the 5000 m speed and vLT with high accuracy (5000 m speed: 
R2 = 0.90; vLT: R2 = 0.96, p < 0.001).
Sprint-trained athletes had significantly higher Maximal Speed (MS) (p < 0.001) and achieved this speed at a 
significantly longer distance (p = 0.003). Significant differences were also observed in  EMAnS, 50 m sprint perfor-
mance (p < 0.001), and peak post-exercise BLa (p = 0.005) in the 50 m sprint run test (Table 5).
Limitations
In general, the present study had no gold standard technique to validate anaerobic techniques, which may be 
presented as one of the limitations. Although there are other anaerobic techniques, such as, cycling or jumping, 
these norms are activity specific and may not accurately predict the anaerobic energy of runners or athletes 
involved in running. The present investigation’s results could only be compared to a similar technique, Bundle’s 
et al.21 anaerobic speed reserve (AnSR). The comparison in results indicated a high correlation between both 
methods, which indicated that MAS may also predict accurate all-out run performances. However, the accuracy 
of MAS to categorize middle distance athletes was not reported. Also, the techniques used for MAS in this study 
was different from Bundle’s use of MAS and utilizing MAS in the  RERI18 had a lower error for prediction. The 
backward validation with lower error in prediction values was the only way to validate MAS. In future, MAS 
could be used to validate other similar anaerobic techniques.
In addition, the effect of training on MAS was not determined. Perhaps for future studies, the effect of differ-
ent types of training, such as sprint or endurance or a combination of both, on MAS can be studied. Therefore, 
extending the accuracy of MAS in significantly differentiating middle distance athletes may increase the sensitiv-
ity of the model to detect even small changes in energy.
Discussion
The results from this study confirmed the hypothesis that MAS is more accurate to be measured at %v ˙VO
2max than at v ˙VO2max. The determination of MAS required a subtraction of  Tlim ˙VO2maxconverted at v ˙VO2max from 
 TlimVsub%95. This equation eliminated the anaerobic energy contribution. The concept of this study is therefore 
unique as the MAS determination has very little anaerobic contribution and has revealed low errors in predict-
ing performance  timings18.
Validation of MAS. 
MAS was obtained at 92.45 ± 1.47%v ˙VO2max and 89.27 ± 3.56%v ˙VO2max for endurance-
trained and sprint-trained athletes respectively, confirming the hypothesis that MAS should be obtained at a per-
centage of v ˙VO2max rather than at v ˙VO2max. Studies have determined higher anaerobic energy at  Tlimv ˙VO2max that 
was verified by a non-significant difference between BLa at v ˙VO2max ( BLav ˙VO2max) and BLa at ˙VO2max (BLa ˙VO2max
)1,2,21,26. Similarly, no significant difference was found in anaerobic energy contribution between  Tlim100%v ˙VO2max 
(15.1 mmol·L −1),  Tlim120 (15.7 mmol·L−1) and  Tlim140 (15.1 mmol·L−1)16.  Tlimv ˙VO2max (269 ± 77 s) was also sig-
nificantly correlated (r = − 0.52, p < 0.05) to  Tlim120v ˙VO2max (86 ± 25 s) and to the blood pH after  Tlim120%v ˙VO2max 
(r = − 0.68, p < 0.05).
On the contrary,  EMAS in this study was obtained at MAS. ˙VO2 at MAS (50.69 ± 4.69 ml·kg−1·min−1) was found 
to be at 96.08 ± 2.51% ˙VO2max, which was not significantly different from 95% ˙VO2max (50.18 ± 5.19 ml·kg−1·min−1). 
As most athletes did not reach  EMAS at speeds of 14.10 km·h−1 which was just below MAS (14.64 km·h−1), MAS 
seems to be the minimal intensity of the slow component of ˙VO2. Additionally, MAS in this study was obtained 
at 91.08 ± 2.97%v ˙VO2max for total cohort, which was similar to other studies where most athletes achieved ˙VO2max 
at 91%v ˙VO2max
30. It was found that endurance-trained athletes in their study ( ˙VO2max = 60.7 ml·kg−1·min−1, v ˙VO
2max = 20 km·h−1) achieved approximately 99% ˙VO2max at 90%v ˙VO2max (18.3 km·h−1)31. This is close to 92.45%v ˙VO
2max at MAS among endurance-trained athletes in the present investigation. These studies suggest that submaxi-
mal speed is sufficient for achieving an increase in ˙VO2max and should be used for  training32. These findings 
support the validity of MAS, which is the minimal speed at which  EMAS is determined.
Table 5.  Maximal speed of endurance-trained and sprint-trained athletes. Values are in means ± SD. MS 
Maximal speed, DistanceMS Distance at which MS determined, BLa50 m Peak post-exercise blood lactate after 
50 m sprint run test. **p < 0.01, ***p < 0.001: Indicates significant difference between endurance-trained and 
sprint-trained athletes.
Variables
Endurance-trained
Sprint-trained
N
12
8
MS (km·h−1)
29.26 ± 1.33
35.21 ± 1.90***
DistanceMS (m)
36.29 ± 3.08
41.05 ± 3.14**
BLa50 m (mmol·L-1)
4.16 ± 0.83
5.53 ± 1.17**
50 m (s)
7.38 ± 0.45
6.38 ± 0.43***
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In addition,  BLaMAS in this study was significantly lesser than BLav ˙VO2 max and BLa ˙VO2 max. This could be due 
to the slow component of ˙VO2 at a slower speed, which is directly related to the recruitment of less efficient fast 
twitch  fibers30, anaerobic energy utilization, and to the intensity of  exercise33–35. The decrement of anaerobic 
energy with increasing duration at  TlimMAS compared to  Tlimv ˙VO2max could lead to lower  BLaMAS compared to 
BLav ˙VO2max. It was also determined that there was significant correlation between the slow component of ˙VO2 
with indices of anaerobic performance (WAnT’s peak power; r = 0.77, p < 0.01)36. Since there is an inverse relation-
ship between TA ˙VO2max and exercise  intensity37, TA ˙VO2max would have been higher at  TlimMAS as compared to 
 Tlimv ˙VO2max.  EMAS would have been attained in the later part of the run, which may minimize anaerobic energy 
contribution. This was shown in the present study and confirmed that MAS calculated was accurate.
MAS between endurance-trained and sprint-trained athletes. 
This study also found that sprint-
trained athletes had significantly lower MAS compared to endurance-trained athletes. This was evident in their 
vLT, ˙VO2max, and v ˙VO2max variables. Endurance training increases ˙VO2max by increasing cardiac stroke volume, 
blood volume, capillary density, and mitochondrial density in trained  muscles35, allowing endurance-trained 
athletes to have higher ˙VO2max, vLT, and v ˙VO2max compared to sprint-trained athletes.
Additionally, MAS had comparatively higher significant correlations with CS, vLT, 5000 m,  TlimυΔ50 + 5%v ˙VO
2max, and Vsub%95 compared to v ˙VO2max. Furthermore, MAS was a stronger predictor of 5000 m and vLT. This 
was similar to a study conducted by Blondel, Berthoinm Billat & Lensel (2001), who also found significant cor-
relations between 90%v ˙VO2max and CS (r = 0.69, p < 0.05)16. Additional analysis found that there was a significant 
negative correlation with maximal speed reserve (MSR; difference between MS and CS; r = 0.79, p ≤ 0.001). This 
relationship is consistent with previous studies who found that endurance-trained athletes with lower MSR 
achieved vLT and CS at higher speeds and had lower MAnS compared to  sprinters16,38. These findings support the 
utility of MAS in predicting performances in most running events and may suggest more accurate performance 
prediction at MAS rather than at v ˙VO2max.
Conclusion
In conclusion, this study aimed to determine the intensity at which aerobic energy contribution is at maximal. 
MAS in this study was found to be at 92.45 ± 1.47%v ˙VO2max for endurance trained athletes, 89.27 ± 3.56%v ˙VO
2max for sprint trained athletes, and 91.08 ± 2.97%v ˙VO2max among the total cohort. This accurately represented 
 EMAS with minimal contribution from anaerobic energy sources, thus confirming the hypothesis that MAS is 
more accurate at %v ˙VO2max rather than at v ˙VO2max. MAS for endurance-trained athletes were also significantly 
higher compared to sprint-trained athletes, indicating that MAS can differentiate between the types of athletes. 
Furthermore, MAS was found to significantly correlate with aerobic performance variables, and this suggest that 
submaximal speed is sufficient for training athletes. Regardless the profile of the individual, recreational athletes, 
collegiate athletes, elite athletes, coaches, and sports practitioners may utilize this MAS calculation to accurately 
derive the athlete’s individual main energy contribution source (anaerobic or aerobic energy source). Coaches 
may use their athletes’ MAS to prescribe training workouts that are specifically catered to them, which will 
predict an accurate sporting performance. Therefore, this new MAS framework demonstrates that the accurate 
calculation of MAS can accurately predict run performances at lower errors.18
Received: 22 February 2023; Accepted: 20 March 2023
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Acknowledgements
Authors would like to thank all participants for volunteering in this study and researchers for collecting data. 
The results of this study are presented clearly, honestly, and without fabrication, falsification, or inappropriate 
data manipulation, and statement that results of the present study. This research was funded by the National 
Institute of Education, Nanyang Technological University, Singapore, Research Support for Senior Academic 
Administrator Grant (RS-SAA 13/17 GB; RS 13/10 GB), and National Institute of Education Academic Research 
Fund Grant (RI 6/11 GB).
Author contributions
G.B. and M.K.L. conceptualized and designed the study. G.B. and M.K.L. collected the data with help of research-
ers; G.B., M.K.L., P.B., and N.Y.C. analyzed the data; and all authors interpreted the data. All authors contributed 
to the writing, review, and editing of the manuscript. All authors have read and agreed to the published version 
of the manuscript.
Competing interests 
The authors declare no competing interests.
Additional information
Correspondence and requests for materials should be addressed to G.B.
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© The Author(s) 2023

Determination, measurement, and validation of maximal aerobic speed.
Balasekaran, Govindasamy,Loh, Mun Keong,Boey, Peggy,Ng, Yew Cheo