Walking slope and heavy backpack loads affect torso muscle activity and kinematics

The independent effects of sloped walking or carrying a heavy backpack on posture and torso muscle activations have been reported. While the combined effects of sloped walking and backpack loads are known to be physically demanding, how back and abdominal muscles adapt to walking on slopes with heavy load is unclear. This study quantified three-dimensional pelvis and torso kinematics and muscle activity from longissimus, iliocostalis, rectus abdominis, and external oblique during walking on 0° and ± 10° degree slopes with and without backpack loads using two different backpack configurations (hip-belt assisted and shoulder-borne). Iliocostalis activity was greater during downhill and uphill compared to level walking, but longissimus was only greater during uphill. Rectus abdominis activity was greater during downhill and uphill compared to level, while external oblique activity decreased as slopes progressed from down to up. Longissimus, but not iliocostalis, activity was reduced during both backpack configurations compared to walking with no pack. Hip-belt assisted load carriage required less rectus abdominis activity compared to using shoulder-borne only backpacks; however, external oblique was not influenced by backpack condition. Our results revealed different responses between iliocostalis and longissimus, and between rectus abdominis and external obliques, suggesting different motor control strategies between anatomical planes.     

Optimal handgrip height of four-wheeled walker on various road conditions to reduce muscular load for elderly users with steady walking

A four-wheeled walker is a valuable tool for assisting elderly persons with walking. The handgrip height is one of the most important factor determining the usefulness of the walker. However, the optimal handgrip height for elderly users has not been considered from a biomechanical viewpoint. In this study, the handgrip height was optimized by a two-dimensional mechanical model to reduce muscular loads in the lower body as well as in the upper body with various road conditions during steady walking. A critical height of the handgrip existed at 48% of the body height for the user regardless of gender and body dimension. A lower handgrip relieved muscular load for stooping users with a lower standing height. The stooping user pushed the handgrip strongly in the perpendicular direction by leaning the upper body on the walker. However, upright users with a higher standing height should use a four-wheeled walker with a higher handgrip for maintaining his or her upright posture. For downhill movement, the optimal handgrip height depended on the slope angle and the friction coefficient between the road and the wheels of the walker. On a low-friction downhill such as asphalt with a steeper slope angle, the user was required to maintain an erect trunk with a higher handgrip and to press on the handgrip strongly in the perpendicular direction. Movement on a low-friction road was easier for users on a flat road and an uphill road, but it compelled distinct effort from users when moving downhill.     

Segment lengths influence hill walking strategies

Segment lengths are known to influence walking kinematics and muscle activity patterns. During level walking at the same speed, taller individuals take longer, slower strides than shorter individuals. Based on this, we sought to determine if segment lengths also influenced hill walking strategies. We hypothesized that individuals with longer segments would display more joint flexion going uphill and more extension going downhill as well as greater lateral gastrocnemius and vastus lateralis activity in both directions. Twenty young adults of varying heights (below 155 cm to above 188 cm) walked at 1.25 m/s on a level treadmill as well as 6° and 12° up and downhill slopes while we collected kinematic and muscle activity data. Subsequently, we ran linear regressions for each of the variables with height, leg, thigh, and shank length. Despite our population having twice the anthropometric variability, the level and hill walking patterns matched closely with previous studies. While there were significant differences between level and hill walking, there were few hill walking variables that were correlated with segment length. In support of our hypothesis, taller individuals had greater knee and ankle flexion during uphill walking. However, the majority of the correlations were between tibialis anterior and lateral gastrocnemius activities and shank length. Contrary to our hypothesis, relative step length and muscle activity decreased with segment length, specifically shank length. In summary, it appears that individuals with shorter segments require greater propulsion and toe clearance during uphill walking as well as greater braking and stability during downhill walking.     

Zigzagging: theoretical insights on climbing strategies

Human and animal trails on steep hillsides often exhibit dramatic switchbacks and shortcuts. Helbing et al. have recently examined the emergence of human trail systems on flat terrains while Minetti and Margaria established the effect of gradients on human metabolic efficiency. In this paper we use these ideas to develop a semi-quantitative theoretical model of the behaviour of humans moving on a terrain with relief. The model determines the direction of movement by minimising metabolic cost per unit of distance in a desired direction. The structure of the theory resembles the Landau Theory of Phase Transitions, much used in theoretical physics. We find that both hairpin bends (switchbacks) and shortcuts appear as efficient strategies for downhill walkers, while uphill walkers retain switchbacks. For weakly inclined slopes, the best strategy involves walking directly uphill or downhill. For sufficiently steep slopes, however, we find that the best strategy should undergo a transition to a broken symmetry solution corresponding to the switchback trail patterns typical of rugged environments. The critical slope at which this transition takes place should be less steep for uphill and downhill walkers. The theory should be amenable to empirical investigation. Amongst other applications, this model will enable us to generalize the work of previous authors to real landscapes, eventually permitting the reconstruction of ancient patterns of movement in archaeological landscapes.     

Mechanical work performed by the individual legs during uphill and downhill walking

Previous studies of the mechanical work performed during uphill and downhill walking have neglected the simultaneous negative and positive work performed by the leading and trailing legs during double support. Our goal was to quantify the mechanical work performed by the individual legs across a range of uphill and downhill grades. We hypothesized that during double support, (1) with steeper uphill grade, the negative work performed by the leading leg would become negligible and the trailing leg would perform progressively greater positive work to raise the center of mass (CoM), and (2) with steeper downhill grade, the leading leg would perform progressively greater negative work to lower the CoM and the positive work performed by the trailing leg would become negligible. 11 healthy young adults (6 M/5 F, 71.0±12.3 kg) walked at 1.25 m/s on a dual-belt force-measuring treadmill at seven grades (0, ±3, ±6, ±9°). We collected three-dimensional ground reaction forces (GRFs) and used the individual limbs method to calculate the mechanical work performed by each leg. As hypothesized, the trailing leg performed progressively greater positive work with steeper uphill grade, and the leading leg performed progressively greater negative work with steeper downhill grade (p<0.005). To our surprise, unlike level-ground walking, during double support the leading leg performed considerable positive work when walking uphill and the trailing leg performed considerable negative work when walking downhill (p<0.005). To understand how humans walk uphill and downhill, it is important to consider these revealing biomechanical aspects of individual leg function and interaction during double support.     

Optimal rate of work for mountaineers

The physiological responses of seven young male highlanders were recorded at high altitude while they were carrying loads (0, 25, 35, 45, and 55 kg) on snow at different speeds, supporting the loads on their backs by circular straps around the forehead. The rates of work calculated from the gross weight (body weight plus actual load in kg) multiplied by the speed of walking, m.min-1, ranged from 4,460 to 8,440 kg.m.min-1. The relationship between the rate of work and energy expenditure was rectilinear within the present range of values. The oxygen consumption (51.6 and 59.7 ml.min-1.kg-1 BW) for 55-kg load (at 4.09 and 4.64 km.h-1) possibly reached maximal aerobic capacity. At higher energy output at high altitude the subjects were exhausted after a short period of work. The proportion of increase of oxygen consumption per kg gross weight carried or per kg.m was almost constant up to a 55-kg experimental load. It is suggested that for day-to-day operations work should not be undertaken at more than 30-40% of maximal work capacity; a rate of work around 4,000 kg.m.min-1 (25-30 kg actual load at 3.0 to 3.5 km.h-1) may be considered as optimal for highlanders and porters at high altitude.     

Trekking poles increase physiological responses to hiking without increased perceived exertion

Trekking poles are used by hikers for improved stability and lowered leg fatigue due to increased upper body muscle involvement. However, the weight of the poles and exaggerated upper body movement when using poles may increase total energy expenditure at a given walking speed. Few studies have investigated the physiological responses of hiking with trekking poles outside the laboratory setting. The purposes of this study were to determine if trekking poles altered physiological responses to hiking on varied terrain, and whether responses between trials were dependent on the grade of the terrain. Fourteen recreational hikers completed four hiking trials over a course that included sustained sections of flat (0 +/- 1% grade), steep uphill (>10% grade), gradual uphill (5% grade), gradual downhill (-5% grade) and steep downhill (<-10% grade) terrain. Subjects walked at a self-selected speed that was matched across trials using time-splits and a metronome. Two trials were conducted with hiking poles and two without poles. [latin capital V with dot above]O2 was significantly elevated (p <0.05) during the pole trials (1502.9 +/- 510.7 ml/min) compared to the no-pole trials (1362.4 +/- 473.2 ml/min). Similarly, ventilatory efficiency ([latin capital V with dot above]E) (43.1 +/- 9.6; 38.3 +/- 10.1 L/min) and heart rate (HR) (112.1 +/- 9.7; 105.7 +/- 10.4 bt/min) were significantly higher during the pole trials than the no-pole trials. However, ratings of perceived exertion (RPE) was not altered by pole condition (8.5 +/- 0.7; 8.4 +/- 0.8). Comparisons within each grade revealed significantly higher physiological responses for [latin capital V with dot above]O2, [latin capital V with dot above]E and HR in the pole-condition at all grades, with no significant variable*grade interactions. RPE measures were not significantly different between pole trials at any grade. These data suggest that trekking poles may be a beneficial tool for increasing caloric expenditure, as energy production increased during exercise without increased perceptions of effort.     

Effects of load and gradient on energy cost of running

This study quantified the interaction of electromyography (EMG) obtained from the vastus lateralis and metabolic energy cost of running (C(r); mL·[mass+load](-1)·meter(-1)), an index of running economy, during submaximal treadmill running. Experiments were conducted with and without load on the back on a motor-driven treadmill on the downhill, level and uphill slopes. The obtained EMG was full-wave rectified and integrated (iEMG). The iEMG was divided into eccentric (ECC) and concentric (CON) phases with a foot sensor and a knee-joint goniometer. The ratio of ECC to CON (ECC/CON ratio) was regarded as the muscle elastic capacity during running on each slope. The C(r) was determined as the ratio of the 2-min steady-state VO(2) to the running speed. We found a significant decrease in the C(r) when carrying the load at all slopes. The ECC/CON ratio was significantly higher in the load condition at the downhill and level slopes, but not at the uphill slope. A significant gradient difference was observed in the C(r) (downuphill). Thus, an alteration of Cr by the gradient and load was almost consistent with that of the ECC/CON ratio. The ECC/CON ratio, but not the rotative torque (T) functioning around the center of body mass, significantly correlated with C(r) (r=-0.41, p<0.05). These results indicated that the ECC/CON ratio, rather than T, contributed to one of the energy-saving mechanisms during running with load.     

Differential serial sarcomere number adaptations in knee extensor muscles of rats is contraction type dependent.

Sarcomerogenesis, or the addition of sarcomeres in series within a fiber, has a profound impact on the performance of a muscle by increasing its contractile velocity and power. Sarcomerogenesis may provide a beneficial adaptation to prevent injury when a muscle consistently works at long lengths, accounting for the repeated-bout effect. The association between eccentric exercise, sarcomerogenesis and the repeated-bout effect has been proposed to depend on damage, where regeneration allows sarcomeres to work at shorter lengths for a given muscle-tendon unit length. To gain additional insight into this phenomenon, we measured fiber dynamics directly in the vastus lateralis (VL) muscle of rats during uphill and downhill walking, and we measured serial sarcomere number in the VL and vastus intermedius (VI) after chronic training on either a decline or incline grade. We found that the knee extensor muscles of uphill walking rats undergo repeated active concentric contractions, and therefore they suffer no contraction-induced injury. Conversely, the knee extensor muscles during downhill walking undergo repeated active eccentric contractions. Serial sarcomere numbers change differently for the uphill and downhill exercise groups, and for the VL and VI muscles. Short muscle lengths for uphill concentric-biased contractions result in a loss of serial sarcomeres, and long muscle lengths for downhill eccentric-biased contractions result in a gain of serial sarcomeres.     

Ground reaction forces during downhill and uphill running

We investigated the normal and parallel ground reaction forces during downhill and uphill running. Our rationale was that these force data would aid in the understanding of hill running injuries and energetics. Based on a simple spring-mass model, we hypothesized that the normal force peaks, both impact and active, would increase during downhill running and decrease during uphill running. We anticipated that the parallel braking force peaks would increase during downhill running and the parallel propulsive force peaks would increase during uphill running. But, we could not predict the magnitude of these changes. Five male and five female subjects ran at 3m/s on a force treadmill mounted on the level and on 3 degrees, 6 degrees, and 9 degrees wedges. During downhill running, normal impact force peaks and parallel braking force peaks were larger compared to the level. At -9 degrees, the normal impact force peaks increased by 54%, and the parallel braking force peaks increased by 73%. During uphill running, normal impact force peaks were smaller and parallel propulsive force peaks were larger compared to the level. At +9 degrees, normal impact force peaks were absent, and parallel propulsive peaks increased by 75%. Neither downhill nor uphill running affected normal active force peaks. Combined with previous biomechanics studies, our normal impact force data suggest that downhill running substantially increases the probability of overuse running injury. Our parallel force data provide insight into past energetic studies, which show that the metabolic cost increases during downhill running at steep angles.     

Exploring Muscle Activation during Nordic Walking: A Comparison between Conventional and Uphill Walking

Nordic Walking (NW) owes much of its popularity to the benefits of greater energy expenditure and upper body engagement than found in conventional walking (W). Muscle activation during NW is still understudied, however. The aim of the present study was to assess differences in muscle activation and physiological responses between NW and W in level and uphill walking conditions. Nine expert Nordic Walkers (mean age 36.8±11.9 years; BMI 24.2±1.8 kg/m²) performed 5-minute treadmill trials of W and NW at 4 km/h on inclines of 0% and 15%. The electromyographic activity of seven upper body and five leg muscles and oxygen consumption (VO₂) were recorded and pole force during NW was measured. VO₂ during NW was 22.3% higher at 0% and only 6.9% higher at 15% than during W, while upper body muscle activation was 2- to 15-fold higher under both conditions. Lower body muscle activation was similarly increased during NW and W in the uphill condition, whereas the increase in erector spinae muscle activity was lower during NW than W. The lack of a significant increase in pole force during uphill walking may explain the lower extra energy expenditure of NW, indicating less upper body muscle activation to lift the body against gravity. NW seemed to reduce lower back muscle contraction in the uphill condition, suggesting that walking with poles may reduce effort to control trunk oscillations and could contribute to work production during NW. Although the difference in extra energy expenditure between NW and W was smaller in the uphill walking condition, the increased upper body muscle involvement during exercising with NW may confer additional benefit compared to conventional walking also on uphill terrains. Furthermore, people with low back pain may gain benefit from pole use when walking uphill.     

Hypnotic manipulation of effort sense during dynamic exercise: cardiovascular responses and brain activation.

The purpose of this investigation was to hypnotically manipulate effort sense during dynamic exercise and determine whether cerebral cortical structures previously implicated in the central modulation of cardiovascular responses were activated. Six healthy volunteers (4 women, 2 men) screened for high hypnotizability were studied on 3 separate days during constant-load exercise under three hypnotic conditions involving cycling on a 1) perceived level grade, 2) perceived downhill grade, and 3) perceived uphill grade. Ratings of perceived exertion (RPE), heart rate (HR), blood pressure (BP), and regional cerebral blood flow (rCBF) distributions for several sites were compared across conditions using an analysis of variance. The suggestion of downhill cycling decreased both the RPE [from 13 +/- 2 to 11 +/- 2 (SD) units; P < 0.05] and rCBF in the left insular cortex and anterior cingulate cortex, but it did not alter exercise HR or BP responses. Perceived uphill cycling elicited significant increases in RPE (from 13 +/- 2 to 14 +/- 1 units), HR (+16 beats/min), mean BP (+7 mmHg), right insular activation (+7.7 +/- 4%), and right thalamus activation (+9.2 +/- 5%). There were no differences in rCBF for leg sensorimotor regions across conditions. These findings show that an increase in effort sense during constant-load exercise can activate both insular and thalamic regions and elevate cardiovascular responses but that decreases in effort sense do not reduce cardiovascular responses below the level required to sustain metabolic needs.     

The energy cost of common tasks in rural Nepal: levels of energy expenditure compatible with sustained physical activity

Three hundred and six measurements of energy expenditure by indirect calorimetry of sitting at rest and self-paced activity were made on 41 men, 48 women and 6 adolescents in a mountain village of Nepal. Except for walking and carrying uphill, measured activities fell within the range of values for light to moderate effort, despite appearing physically demanding. Villagers tended to reduce travel speed when carrying heavy loads (54-102% of body mass on various inclines), averaging a moderate level of energy expenditure which could be sustained throughout the day. Such moderately demanding work was also assumed by pregnant, lactating women and young adolescents. Pregnant women worked more slowly at some tasks, but did not differentiate themselves from their non-pregnant, non-lactating counterparts for travel on the mountain side.     

Human muscle function following prolonged eccentric exercise

4 subjects performed repeated eccentric contractions with leg extensors during prolonged downhill walking (-25% gradient) at 6.44 km.h-1 until collapse due to muscle weakness (range of exercise duration 29 to 40 min). During the exercise oxygen uptake rose progressively from approximately 45% of the previously determined VO2max at 10 min to approximately 65% at the end of the exercise. Following the exercise there was an immediate, significant, and sustained reduction in maximal voluntary isometric contraction, and short term (anaerobic) power output measured concentrically on an isokinetic ergometer. These reductions in muscle function persisted for 96 hours post exercise, and were reflected by significant reductions in the tension generated at low frequency (20 Hz) relative to higher frequency (50 Hz) percutaneous stimulation of the quadriceps. All four subjects showed an increase in plasma levels of creatine kinase post eccentric exercise. Performing concentric contractions by walking uphill for one hour at a significantly greater metabolic cost failed to induce comparable reductions in muscle function. These results provide evidence for the consequences of prolonged eccentric work upon dynamic function which complements earlier reports of structural, enzymatic, and static function changes.     

Changes in latitude: overwintering survival of two Lilioceris cheni (Coleoptera: Chrysomelidae) biotypes in Florida

Lilioceris cheni is a successful biological control agent on the invasive yam, Dioscorea bulbifera in many areas in Florida, Georgia, Alabama and Louisiana. Two biotypes are available for release and come from significantly different centres of origin. The Nepalese biotype was collected at higher altitude and latitude sites, whereas the Chinese biotype was collected at slightly lower latitude and lower altitude. We hypothesised that Nepalese beetles would survive winter better in north Florida and that Chinese beetles would overwinter better in subtropical south Florida. We established sites in Homestead, Fort Pierce, Gainesville and Tallahassee, Florida to gauge the overwintering survival of each biotype. Beetles that overwintered in each site for one to three seasons were collected and followed to assess their reproductive capacity. In the final year of the experiment, we extracted fat bodies to determine effects of biotype and site. Nepalese beetles overwintered significantly better overall. Beetles survived better in the first study year (2013–2014). Both biotypes reproduced very well after surviving winter and beetles in Fort Pierce survived better than beetles in other regions and maintained a higher fat body. Nepalese beetles may have a wider ecological envelope – a decided advantage for a large region such as peninsular Florida. We suggest that current release programmes incorporate Nepalese beetles into their protocol to increase overwinter survival and establishment.     

Effect of training on skeletal muscle injury from downhill running in rats

Experiments were conducted to test the hypothesis that injury to skeletal muscle in rats resulting from prolonged downhill running is prevented to a greater extent by prior downhill training than by either uphill or level training. Changes in plasma creatine phosphokinase (CPK) activity and glucose-6-phosphate dehydrogenase (G-6-PDase) activity in the soleus (S), vastus intermedius (VI), and medial head of triceps brachii (TM) muscles were evaluated as markers of muscle injury 48 h after 90 min of intermittent downhill running (16 m . min -1). Prior to this acute downhill run, groups of rats were trained by either downhill (-16 degrees), level (0 degrees), or uphill (+16 degrees) running (16 m . min -1) for 30 min/day. Training duration was either 5 days or 1 day. A training effect (i.e., reduced muscle injury) was indicated if muscle G-6-PDase or plasma CPK activity in a trained group following the 90-min downhill run was not different from that of nonexercised control animals and/or if it was lower than that of nontrained runners. A significant training effect was achieved in all three muscles with 5 days of either downhill or level training, but only in S after 5 days of uphill training. Elevation of plasma CPK activity was prevented by 5 days of training on all three inclines.(ABSTRACT TRUNCATED AT 250 WORDS)     

Metabolic cost of generating muscular force in human walking: insights from load-carrying and speed experiments.

We sought to understand how leg muscle function determines the metabolic cost of walking. We first indirectly assessed the metabolic cost of swinging the legs and then examined the cost of generating muscular force during the stance phase. Four men and four women walked at 0.5, 1.0, 1.5, and 2.0 m/s carrying loads equal to 0, 10, 20, and 30% body mass positioned symmetrically about the waist. The net metabolic rate increased in nearly direct proportion to the external mechanical power during moderate-speed (0.5-1.5 m/s) load carrying, suggesting that the cost of swinging the legs is relatively small. The active muscle volume required to generate force on the ground and the rate of generating this force accounted for >85% of the increase in net metabolic rate across moderate speeds and most loading conditions. Although these factors explained less of the increase in metabolic rate between 1.5 and 2.0 m/s ( approximately 50%), the cost of generating force per unit volume of active muscle [i.e., the cost coefficient (k)] was similar across all conditions [k = 0.11 +/- 0.03 (SD) J/cm3]. These data indicate that, regardless of the work muscles do, the metabolic cost of walking can be largely explained by the cost of generating muscular force during the stance phase.     

Transference of 3D accelerations during cross country mountain biking

Investigations into the work demands of Olympic format cross country mountain biking suggest an incongruent relationship between work done and physiological strain experienced by participants. A likely but unsubstantiated cause is the extra work demand of muscle damping of terrain/surface induced vibrations. The purpose of this study was to describe the relationship between vibration mechanics and their interaction with terrain, bicycle and rider during a race pace effort on a cross country mountain bike track, on both 26″ and 29″ wheels. Participants completed one lap of a cross country track using 26″ and 29″ wheels, at race pace. Power, cadence, speed, heart rate and geographical position were sampled and logged every second for control purposes. Tri-axial accelerometers located on the bicycle and rider, recorded accelerations (128 Hz) and were used to quantify vibrations experienced during the whole lap and over terrain sections (uphill and downhill). While there were no differences in power output (p=0.3062) and heart rate (p=0.8423), time to complete the lap was significantly (p=0.0061) faster on the 29″ wheels despite increased vibrations in the larger wheels (p=0.0020). Overall accelerometer data (RMS) showed location differences (p<0.0001), specifically between the point of interface of bike–body compared to those experienced at the lower back and head. The reduction in accelerations at both the lower back and head are imperative for injury prevention and demonstrates an additional non-propulsive, muscular, challenge to riding. Stress was greatest during downhill sections as acceleration differences between locations were greater when compared to uphill sections, and thus possibly prevent the recovery processes that may occur during non-propulsive load.     

The effect of uphill and downhill walking on gait parameters: A self-paced treadmill study

It has been shown that gait parameters vary systematically with the slope of the surface when walking uphill (UH) or downhill (DH) (Andriacchi et al., 1977; Crowe et al., 1996; Kawamura et al., 1991; Kirtley et al., 1985; McIntosh et al., 2006; Sun et al., 1996). However, gait trials performed on inclined surfaces have been subject to certain technical limitations including using fixed speed treadmills (TMs) or, alternatively, sampling only a few gait cycles on inclined ramps. Further, prior work has not analyzed upper body kinematics. This study aims to investigate effects of slope on gait parameters using a self-paced TM (SPTM) which facilitates more natural walking, including measuring upper body kinematics and gait coordination parameters.Gait of 11 young healthy participants was sampled during walking in steady state speed. Measurements were made at slopes of +10°, 0° and −10°. Force plates and a motion capture system were used to reconstruct twenty spatiotemporal gait parameters. For validation, previously described parameters were compared with the literature, and novel parameters measuring upper body kinematics and bilateral gait coordination were also analyzed.Results showed that most lower and upper body gait parameters were affected by walking slope angle. Specifically, UH walking had a higher impact on gait kinematics than DH walking. However, gait coordination parameters were not affected by walking slope, suggesting that gait asymmetry, left-right coordination and gait variability are robust characteristics of walking. The findings of the study are discussed in reference to a potential combined effect of slope and gait speed. Follow-up studies are needed to explore the relative effects of each of these factors.     

Distance estimation in the third dimension in desert ants

Desert ants of the genus Cataglyphis perform large-scale foraging excursions from which they return to their nest by path integration. They do so by integrating courses steered and the distances travelled into a continually updated home vector. While it is known that the angular orientation is based on skylight cues, it still is largely enigmatic how the ants measure distances travelled. We extended the ants' task into the third dimension by training them to walk within an array of uphill and downhill channels, and later testing them on flat terrain, or vice versa. In these tests the ants indicated homing distances that did not correspond to the distances actually travelled, but to the ground distances; that is, to the sum of the horizontal projections of the uphill and downhill segments of the ants' paths. These results suggest a much more sophisticated mechanism of distance estimation than hitherto thought. The ants must be able to measure the slopes of undulating terrain and to integrate this information into their "odometer" for the distance estimation process.