A biomechanical model for estimating moments of force at hip and knee joints in the barbell squat

Introduction

The barbell squat is a complex, mass load bearing multi-articular exercise movement. It is the basic lower body exercise prescribed in training programs for many sports even though it is unpopular with most athletes and is often performed inexpertly. One of the major problems when performing a full squat with heavy weights is that there appears to be excessive loading in the bottom part of the movement. At the same time loading through the top range of the movement seems inadequate.

This study examines the extent to which these effects may be attributable to changing values of resistive torque in moving from deep flexion to full extension of the hip and knee joints, i.e., to changes in limb geometry. A basic biomechanical model of the squat has been developed to calculate moments of force or torque applied about the axes of the hip and knee joints at various angles of those joints. I am not aware of any previous comparable study of the free weight squat.


The Model

A mathematically scaled model of a person of 180cm height and 100kg body weight was created consisting of four linked segments. These were the upper body or HAT (head, arms and trunk) assumed to be a rigid member; the thighs; the shanks; and the feet. The lengths of the segments as a percentage of total height were 50, 24, 22, and 4 respectively. Centres of gravity for the thighs and shanks were assumed to be both at 43.3% of segment length measured proximally. The proportion of body weight for the upper body, thighs and shanks was estimated as 68.6%, 20.0% and 8.6% respectively.

In order for stability to be maintained in squatting, the centre of gravity of the system (exerciser's body plus weight bar) must remain directly over the feet. Unless the centre of mass is constantly positioned directly above the ground reaction force vector, a moment would exist and the system would rotate, i.e., tip forward or backward.

To provide a determinate model and to facilitate calculation, a number of simplifying assumptions were used, Firstly, throughout the exercise movement the hip and knee joints move synchronously, i.e., at any point their angles are equal. Secondly, the force vector of the weight bar (FWB) was assumed to be located directly above that of the upper body (cgUB). Thirdly, it was assumed that the centre of gravity of the system remains directly above the ankle joint rather than at the midpoint of the foot as is usually and more correctly assumed. Figure 1 shows a simplified free body diagram incorporating the assumptions.

At each observation point throughout the exercise the body is evaluated in a static or constant velocity state and therefore can be treated as rigid. Moments of force were calculated for the knee and hip joints using a link-segment model of the form described in Winter (1990).

Other than its contribution to total body mass the weight of the exerciser's feet was ignored. For the present calculations the mass of the loaded weight bar was assumed to be 100kg. Its force (F_WB) contributes to moments about the joints. The vertical reaction force (F_GR) from the floor to the exerciser's feet also provides a force of flexion about the hip and knee joints. The constant velocity assumption means that the ground reaction force is simply the sum of the body mass and the mass of the weight bar, i.e., 200kg in this application of the model.

The range of motion investigated was from deep flexion of 40° for both hip and knee joints to lock-out or full extension at 180°.

Figure 1

Results

Figure 2 shows the moments of force about the hip and knee joints calculated using the model. It can be seen that very high moment values occur in deep squat positions. In fact at 60° flexion of both joints, torque values are 470N.m and 333N.m for the hip and knee joints respectively. In this model the parallel position for the thigh occurs at joint angles of 62.5°. This is the position where the hip and knee joints are furthest from the force vectors of the weight bar and upper body, with the result that torque values for hip and knee joints reach their maxima here at 471N.m and 334N.m respectively.

Below this point it can be seen that torque values are declining, but this effect is counteracted by the fact that the leg extensor muscles are lengthening and therefore increasingly less able to deliver force.

It can also be seen that as the exerciser rises above joint angles of around 90° the torque values decline markedly and approach zero with full extension or lock-out.

I am unaware of any published studies of strength curves for complex exercises like the barbell squat but it can be expected that the leg extensor muscles function most efficiently in the mid range of the exercise movement. The conjunction of such a muscle strength profile with the torque curves shown above means that a heavy load would place the exerciser in a biomechanically disadvantageous position in the deep range of the movement. At the same time there would be inadequate effective activation of the leg extensor muscles through the top range.

Figure 2

It should be noted that the torque values were calculated with the exerciser stationary at each joint position, so they are isometrically determined. Different results would be obtained if measurements were made of actual dynamic movement. Results would also vary if the assumption of synchronised joint angles did not apply. However in both situations similar extreme variations in torque between bottom end and top end positions could be anticipated.

Correcting for variations in joint torque

A number of methods have been developed to improve the efficacy of the squat exercise. The most well known involve the addition of metal chains or rubber bands to the squat apparatus. With the former sections of chain are hung from each end of the weight bar. As the lifter descends links begin to pile on the floor, lessening the effective load and consequently the joint torque.

The usual method of using bands when squatting is to attach one or more heavy rubber bands to each end of the weight bar and anchor them to hooks on the floor. As the lifter rises tension in the bands increases adding to the effective load and the joint torque. However this system has no effect on the torque at the bottom end of the movement. To correct this a reverse band technique is employed. Here the bands from the weight bar are attached to the top of the squat rack or the ceiling. As the lifter descends tension in the bands increases, thereby compensating for the increasing torque in the bottom range.

The MyoQuip ScrumTruk has been developed to overcome the deficiencies in the conventional squat. It solves the problem of excessive variation in torque in two ways. Firstly it is operated in a horizontal body position thus greatly reducing the contribution of the user's own body weight to torque generation. Secondly its use of QuadTorq variable resistance technology compensates for torque variation at both ends of the movement. The ability to make adjustments to the rate of change of load means that the user can experience appropriate load and effective muscle activation through the whole range of movement.

Why tall people can't squat

It is generally recognised that people with long limbs are poor squatters. They often look awkward performing the exercise and the poundages they lift are usually unimpressive. The present study sheds light on why this is so.

Figure 3

Figures 3 and 4 compare the joint moment forces generated in the squat by three lifters of different height. In each case we assume that the lifter weighs 100kg and is squatting a weight bar loaded to 100kg. The assumed body heights are 160cm, 180cm and 200cm. Inspection of the two charts indicates that torque values vary directly with body height. In fact it can be seen that the moments of force at any joint angle are 25% higher for an athlete of 200cm than for one of 160cm. Therefore in the bottom range of the movement they are much more subjected to excessive loading.

Figure 4

There is an additional effect. Given that work can be measured as force times distance, it is obvious that a tall person will rise further and therefore perform more work than a shorter person. Again our 200cm subject is performing 25% more work than their 160cm counterpart.

Thus there are logical reasons for the perceived poor performance of tall people in the barbell squat.

Conclusion

This study has demonstrated that throughout a deep squat movement with heavy loading the moments of force experienced at the hip and knee joints typically vary from excessive to inconsequential. Because of this the leg extensor muscles are likely to be effectively activated for only a minor part of the exercise movement.

It therefore seems appropriate to question the efficacy of the squat as a general exercise for developing leg strength. In particular the wisdom of its use in preparing athletes for participation in sports that themselves have high incidence of back and knee injury must be doubted.

References

Abelbeck, K.G. Biomechanical model and evaluation of a linear motion squat type exercise. J. Strength Conditioning Res. 16: 516-524. 2002.

Robertson, D.G.E., G.E. Caldwell, J. Hamill, G Kamen and S.N. Whittlesey. Research Methods in Biomechanics. Champaign, IL: Human Kinetics, 2004.

Winter, D.A. Biomechanics and Motor Control of Human Movement. New York: John Wiley & Sons, Inc. 2nd Edn. 1990.

Harland force behind the Students

by Aaron Scott*


For much of the winter David Lyons looked a spent force as an International rugby player. Throughout the Super 14 season his form was slated by critics: he was too predictable, too one-dimensional, not dynamic enough. He found himself relegated to the Waratah's bench. In May he was a shock omission from the Wallabies training squad. He didn't play a Test all winter. Only gradually did it emerge that he had been suffering from a prolapsed disc in his back. Either way, it seemed that the 40-Test veteran and 2004 John Eales medal winner was washed-up at 26.

Enter University's Strength and Conditioning coach, Martin Harland. Lyons' problems were pin-pointed. Two years of injury (groin and back) had eroded his superb physical attributes. Barely able to drag himself through an 80-minute match, Lyons had shunned the gym and the training paddock. His legs had all but atrophied.

Harland decided to settle the prolapsed disc in Lyons' back, redevelop his core strength, then rebuild the dynamism in his legs. Within 13 weeks Lyons was playing a starring role in the Students dramatic victory over Randwick in the Tooheys New Cup Final. He was back in the starting line-up for the Waratahs in the recent APC tournament. He has been named in the 37-man squad for the Wallabies Spring Tour.

"My body is feeling really good," he recently told the Sun-Herald. "My priority was to build my core and back strength, and that feels fine now."

This is a story that says a lot about Lyons. But it is also a story that speaks volumes for Martin Harland. Not that he would admit this.

"David makes it easy for me because he is such a good trainer," says Harland. "He looks after himself, he listens and he's forward thinking in his own programs. I give him a program and he embellishes it - and it's only ever with good things."

The truth is, however, that Harland's skill as a strength and conditioning coach and his exquisite understanding of the physiological make-up of an athlete's body were pivotal in Lyons' rebirth as a footballer and, consequently, in the Students' stunning 2006 success. And this is just one example among many.

"I think there's no coincidence that Sydney University Rugby was struggling after the premierships in '99 and 2000," says Students' outside centre and Waratah, Tom Carter. "Then Marty comes on board, manages an Elite Development Squad and we've won back-to-back premierships over the last two years. We've won, I think, nine premierships out of a possible 14, and won two Club Championships. Marty's Elite Development Squad has basically changed the whole club.

The EDS Carter talks of was established by then-Rugby-Director Todd Louden and Harland back in 2003 as a pre-season fitness, conditioning and skills program. This year 25 elite players will participate in the program that begins in October.

"For me I was playing Australian 7's, weighing 90 kilos and I was physically inept," says Carter. "I was never going to go to the next level. Marty's EDS has certainly changed me physically to a point where I can now compete at that level. It's a feature of 90% of the players that come out of Sydney Uni Football Club - they're physically superior. We go into Super 14 programs so much better off because we're exposed to this high quality training."

These comments give some indication of Harland's contribution to the Football club. His work with the rugby boys, however, is simply one facet of his incredibly varied program.

"Most trainers only work in one sport," says President of Sydney University Sport, Bruce Ross. "Marty is quite amazing because he works across such a broad field. He's working, of course, with our rugby squads, he's had a lot to do with the extraordinary development our rowers have experienced, he's recently worked with the Flames, with the cricketers and, of course, earlier on with Astrid Loch-Wilkinson representing Australia in the bobsleigh."

It's this variety of sports, this vast spread of fitness and strength levels that Harland thrives on.

For years he worked exclusively with elite-level football teams: the Illawarra Steelers, St George-Illawarra Dragons and Sydney Swans. The positions were an exciting divergence for a young sprinter turned Olympic bobsleigher (he competed at the 1988 Calgary Olympics before a severe back injury forced him from the sport in 1989) who completed an Exercise Science degree with first class honours in 1994.

It was the huge amount of research he did in sprinting and power development that saw him snaffled up by the Steelers as a sprint coach in 1995. When the club amalgamated with St George in 1999 his position blossomed into a full-time strength and conditioning role.

In 2000 he shifted codes to AFL where he worked as strength coach for the Sydney Swans.

"It was a lot of fun," says Harland. "It was very different; I'd never had anything to do with the sport before so I really enjoyed it. But AFL is very full-on in terms of what they ask of you."

With the birth of his first child Harland rejected a two-year contract with the Swans and decided to head back to the Andrew Farrar-coached Dragons. It was short-lived. With Nathan Brown's appointment as coach in 2003, Harland's contract was not renewed.

"It put my nose out at first," he says, "but in the end I think it has been for the best."

Harland shifted to the Sydney Academy of Sport where he was contracted to work with the Sydney University Football Club. As the SAS was gradually consumed by the NSW Institute of Sport, Harland's involvement with Sydney University deepened.

None of the higher profile NRL or AFL positions, however, offered the disparate challenges that Harland now faces at Sydney University. And it is this variety, this sheer diversity that Harland revels in.

"With high-level sport everyone is much the same in terms of training age which makes it easier if you know your stuff," says Harland. "You can bash the group and you know what will happen. Here you have a massive training age difference, from guys and girls who have never trained but are still fantastic at their sport, to those who are so highly trained you're really splitting hairs trying to get those physical results.

"And I love the different sports. Some sports I've perhaps watched once - like European Handball - but a scholarship holder will give me a video of a game, tell me what they need and away we go. So I'm always learning as well. You know, high-level coaches - I pick their brains, high-level athletes - I pick their brains, medical staff - I pick their brains. I learn so much here and it keeps me sane. You never fall into a comfort zone, never fall into a rut."

And - with Harland's impeccable understanding of training methods and how they work on a cellular level - it's unlikely that Sydney University's fine stable of athletes will slip into a rut.

*A Media and Communications graduate from Sydney University, Aaron Scott is currently working as a sports journalist for Sydney University Sport. He also writes freelance articles for the Sun-Herald and Inside Sport.