Modelling Energy Demands of Cross-Country Tests in 2-Star to 5-Star Eventing Competitions

Abstract

Eventing is an Olympic equestrian discipline comprising dressage, cross-country, and show jumping, with the cross-country phase imposing the greatest physical demands on horses. This study presents a composite model to estimate energy expenditure during the cross-country phase, integrating physiological data (heart rate-derived VO2 and lactate-based anaerobic estimates) with external workload indicators (GPS-derived speed, elevation, and course complexity). Model development was based on 691 rides from 256 horses across 232 events at 2-star to 5-star competition levels. The analysis showed that terrain, speed variability, and acceleration, largely shaped by course design, significantly affect energy expenditure. Aerobic and anaerobic contributions to power output varied by speed, format, and competition level. The model explained 29% of variance in power output and 91% when accounting for random effects, demonstrating the influence of both external and individual factors. Short-format events exhibited higher anaerobic contributions than long-format events. While the competition level had a modest effect, it reflected increasing technical difficulty and jump size. These findings underline the importance of incorporating both physiological responses and course characteristics in energy assessments. The model supports more targeted conditioning, enhances performance monitoring, and contributes to improved equine welfare by providing a more accurate understanding of workload in cross-country competitions.

Keywords: GPS data; anaerobic demand; cost of transport; cross-country; energy expenditure; eventing; external load; heart rate; internal load; metabolic power.

Figure 1

Power output estimated from 256 horses during 691 cross-country competitions on 2-star (CCI2*), 3-star (CCI3*), 4-star (CCI4*) and 5-star (CCI5*) level based on the power demand calculated from $P{D}_{path}$, $P{D}_{acc}$, and $P{D}_{elev}$. Line of identity (dotted) and regression lines of the linear mixed-effects model are shown separately for different competition levels.

Figure 2

$P{D}_{acc}$ estimated from 394 horses during 1978 cross-country competitions in relation to mean speed. Regression lines of the linear mixed effects model are shown separately for short (CCI-S) and long (CCI-L) competition formats.

Figure 3

Total energy expenditure predicted by the proposed model from GPS data of 394 horses during 1978 cross-country competitions in relation to competition level (2-star to 5-star) and format (short: CCI-S; long: CCI-L).

Figure 4

Power output predicted by the proposed model from GPS data of 394 horses during 1978 cross-country competitions in relation to competition level (2-star to 5-star) and format (short: CCI-S; long: CCI-L).

Figure 5

Anaerobic power output estimated from 256 horses during 691 cross-country competitions in relation to total power output. Regression lines of the linear mixed effects model are shown separately for short (CCI-S) and long (CCI-L) competition formats.

Figure 6

Anaerobic power output estimated from 256 horses during 691 cross-country competitions in relation to competition level (2-star to 5-star) and format (short: CCI-S; long: CCI-L).