Rodger Kram

Purpose To extend the Running Energy Expenditure Estimation (RE3) model for predicting metabolic rates during uphill and downhill running as well as to enhance the Hoogkamer-Taboga-Kram (HTK) equation for estimating metabolic rates during level and uphill running. Methods We combined running metabolic data from an original dataset (n = 62) with individual subject data from 26 studies (n = 424) and group mean data from 12 studies (n = 187). Using this integrated dataset, we derived a new graded running term for the empirical RE3 model and updated the HTK equation coefficients for level and uphill running. We then compared the accuracy and precision of these new equations with the established American College of Sports Medicine (ACSM) and Minetti et al. equations based on the root-mean-square deviation (RMSD). Results Accuracy and precision of estimating level Ṁ were high for the Minetti et al. (RMSD, 1.44 W kg⁻¹), HTK (1.30 W kg⁻¹), and RE3 (1.27 W kg⁻¹) equations, but much worse for the ACSM equation (1.82 W kg⁻¹). Agreement on uphill slopes was highest for the HTK (RMSD, 1.45 W kg⁻¹) and RE3 (1.41 W kg⁻¹) equations with less precision noted for the ACSM (2.17 W kg⁻¹) and Minetti et al. (2.18 W kg⁻¹) equations. When estimating Ṁ during downhill running, the RE3 equation performed marginally better (RMSD, 1.45 W kg⁻¹) than the Minetti et al. equation (1.57 W kg⁻¹). Conclusion The improved RE3 and HTK equations estimate metabolic rates during level and graded running with improved accuracy and precision. We provide a publicly available web-based metabolic rate calculator that simplifies estimation for researchers, practitioners, and runners alike.

Purpose: To extend the Running Energy Expenditure Estimation (RE3) model for predicting metabolic rates during uphill and downhill running as well as to enhance the Hoogkamer-Taboga-Kram (HTK) equation for estimating metabolic rates during level and uphill running. Methods: We combined running metabolic data from an original dataset (n=63) with individual subject data from 26 studies (n=424) and group mean data from 12 studies (n=187). Using this integrated dataset, we derived a new graded running term for the empirical RE3 model and updated the HTK equation coefficients for level and uphill running. We then compared the accuracy and precision of these new equations with the established American College of Sports Medicine (ACSM) and Minetti et al. equations based on the root-mean-square deviation (RMSD). Results: Accuracy and precision of estimating level Ṁ were high for the Minetti et al. (RMSD, 1.44 W·kg ^-1 ), HTK (1.30 W·kg ^-1 ), and RE3 (1.27 W·kg ^-1 ) equations but much worse for the ACSM equation (1.82 W·kg ^-1 ). Agreement on uphill slopes was highest for the HTK (RMSD, 1.45 W·kg ^-1 ) and RE3 (1.41 W·kg ^-1 ) equations with less precision noted for the ACSM (2.17 W·kg ^-1 ) and Minetti et al. (2.18 W·kg ^-1 ) equations. When estimating Ṁ during downhill running, the RE3 equation performed marginally better (RMSD, 1.45 W·kg ^-1 ) than the Minetti et al. equation (1.57 W·kg ^-1 ). Conclusion: The improved RE3 and HTK equations estimate metabolic rates during level and graded running with improved accuracy and precision. We provide a publicly available web-based metabolic rate calculator that simplifies estimation for researchers, practitioners, and runners alike.

The incidence of lower extremity injuries in collegiate distance runners is ∼20%. Identification of a runner sustaining a potential injury remains challenging. This exploratory, cross-institutional study sought to determine whether ground reaction force (GRF) characteristics during steady-state running could identify competitive collegiate distance runners who would later sustain lower extremity injuries. Normative boundaries for 10 GRF variables during braking and propulsion were established for noninjured runners using median ± scaled median absolute deviation. A subanalysis was conducted on runners with and without impact peaks in vertical GRF to mitigate the influence of impact peaks on GRF variables. We hypothesized that prior to injury, runners who later developed an injury would have more GRF variables outside of the normative boundaries than noninjured runners. Using Cliff’s method, a rank-based, nonparametric method for comparing 2 independent groups, we found no statistically significant difference between the number of variables outside the boundaries for injured and noninjured runners overall (P = .17). However, injured runners without impact peaks had more variables outside the normative boundaries than noninjured runners (P < .001). This novel analytical approach demonstrates the potential for preidentifying collegiate distance runners without impact peaks who may be at risk for injury.

In 2023, Faith Kipyegon set the female world record for running one mile (4:07.64). Here, we quantitatively explore if improved aerodynamic drafting could allow her to run just 3.19% faster and thus break the 4-minute mile barrier. Drafting involves other athletes (pacers) running in formation around a designated athlete to reduce the aerodynamic drag force acting on the designated runner. Drafting allows the designated athlete to run faster at the same rate of metabolic energy consumption. Our overall approach was to estimate Kipyegon’s metabolic energy consumption during her mile world record performance. Then, we used empirically established relationships between horizontal resistive force, running velocity and metabolic power to estimate how much faster she could run at the same metabolic power if the aerodynamic force was reduced via drafting. Our calculations suggest that Kipyegon could run ~3:59.37 with drafting provided by one pacer in front and one in back who change out with two other pacers at 800 m.

In 2023, Faith Kipyegon set the female world record for running one mile (4:07.64). Here, we quantitively explore if improved aerodynamic drafting could allow her to run just 3.19% faster and thus break the 4-minute mile barrier. Drafting involves other athletes (pacers) running in formation around a designated athlete to reduce the aerodynamic drag force acting on the designated runner. Drafting allows the designated athlete to run faster at the same rate of metabolic energy consumption. Our overall approach was to estimate Kipyegon’s metabolic energy consumption during her mile world record performance. Then, we used empirically established relationships between horizontal resistive force, running velocity and metabolic power to estimate how much faster she could run at the same metabolic power if the aerodynamic force was reduced via drafting. Our calculations suggest that Kipyegon could run ∼3:59.37 with drafting provided by one pacer in front and one in back who change out with two other pacers at 800 m.