What is a force-time diagram


Biomechanical measurements enable the quantitative recording of motion sequences. The movement is operationalized via the measurement and can therefore be analyzed more precisely. Subjective movement observations can be checked and combined with the biomechanical parameters.

In today's top-class sport in particular, biomechanical investigations play an important role when it comes to optimizing movement techniques. With the help of the quantitative measurement data, the movement can be objectively assessed and assessed. Necessary corrective measures can be controlled much better on the basis of biomechanical measurements.

In school, the theoretical area of ​​biomechanics can be made the subject of considerations in sports theory lessons. Unfortunately, practical implementation of the material taught is usually difficult, biomechanical equipment is missing, physical knowledge is not available or biomechanical topics appear to be too difficult. Many teachers therefore shy away from discussing biomechanical topics and choose training science or other movement science topics. The following article attempts to prepare a subject area of ​​biomechanics, namely the measurement of force, in a clear and practical way for use in sports theory lessons. In some cases, an experimental procedure is even chosen in order to achieve a practical occupation with the material. The necessary equipment is available in most schools or can be obtained relatively easily by students or teachers. Previous physical knowledge is only required to a limited extent.


Forces can have two different effects. If we only observe a deforming effect without the object on which the force acts moving, we speak of a static force. If the body moves, one speaks of a dynamic force effect. We can record and interpret both force effects with biomechanical measuring instruments. In the following, we want to use some very simple examples to make it clear how you can measure force in class, show it in a force-time curve and then interpret it.


Special force measuring platforms (e.g. Kistler measuring pressure plates) are usually used for the biomechanical measurement of force. They enable the recording of force-time courses with high accuracy and a high temporal resolution. Several thousand measurements per second can be made and forces from a few newtons to several kilonewtons can be recorded. Unfortunately, such force plates are so expensive that they can usually only be found in universities. In order to still be able to understand the function and mode of operation of a force measuring platform, one must use other measuring instruments.

A commercially available scale can be of great help here. Scales with an analog display are particularly suitable, since digital scales often do not allow the display to be tracked in the event of somewhat faster movements. On the other hand, the digital scales do not show the post-oscillation during movements on the scales like analog scales. To select a suitable balance, you should therefore do some preliminary experiments and then choose a suitable model.

The balance can be used as a force measuring platform replacement in the classroom. For the tasks described below, optical observation of the scale display or recording with a video camera is possible. If a video camera is to be used, it must have a shutter device, otherwise the scale display cannot be clearly recognized. The video camera can then even be used to assign individual values ​​over time, since 4/100 seconds pass from image to image when a single image is switched on with cameras. In the case of recorders with a jog shuttle, this time span can even be reduced to 2/100.

Of course, such force measurements are not comparable with the results of biomechanical force plates. We cannot determine quantitative results because, for example, post-oscillation of the balance makes an evaluation more difficult. It should be noted that post-oscillations that occur after the end of the movement are not caused by applied forces, but by the inertia of the display instruments. They must therefore be disregarded and students should be made aware of this problem as well. With some balances, you can eliminate the post-oscillation by adding a small braking mechanism. Depending on the technical talent, a scale can be structurally modified accordingly. Despite all of these concerns, scales enable a clear illustration of how force-time curves can be determined. In addition, the experimental procedure in the following results in a greater motivation of the students than with a purely theoretical treatment of the topic. If you are lucky enough to be able to fall back on a force measuring platform at a university, then, of course, qualitatively much better measurements are possible.


The chapter heading already provides the framework for the first two questions. First of all, it must be clarified what force actually is and what a scale or force measuring platform actually measures.

To clarify the question of what force is, one must fall back on the physics knowledge of the students. Force is defined as follows:

F = m * a 556

Force is therefore defined as the product of mass and the acceleration generated by the force. The unit of mass is the kilogram, that of acceleration is meters / seconds2. Newtons are therefore defined by the SI units kg * m / s2.

However, the scale display only shows the mass in kilograms. Physically this is not correct, because ultimately we also measure a force with the scales, namely the weight with which the mass of the body is accelerated by the acceleration of gravity towards the center of the earth. The mass display of the balance must therefore still be multiplied by the magnitude of the acceleration due to gravity in order to arrive at the force acting on it. The direction of the gravitational acceleration also shows that a force is always a directed quantity. It points in one direction and thereby also generates an acceleration in the corresponding direction.

Experiment 1: Our first experiment should be to determine the masses of all students and the associated weight should be calculated:


Mass: 70 kg

Gravitational acceleration: 9.81 m / s2

=> Force: 70 * 9.81 556 = 686.7 N

When we stand on the scales, a student weighing 70 kg generates a counterforce of approx. 700 N through the use of his muscles. This counterforce (supporting force) is directed exactly in the opposite direction to the weight. If the counterforce would be less than 700 N, the body would sink to the ground, if it were greater, the body would lift off the ground. We therefore measure precisely this counterforce on the scales, which can keep the body in an upright position.

If we want to enter the force measured with the scales in a force-time diagram, we have to read the force several times within several seconds, for example, and then enter it in a diagram. For the above case of standing quietly on a scale, the following curve results:

Fig. 1 Force versus time when standing on a scale

Provided the person standing on the scales does not move, the force-time curve shows a curve parallel to the time axis. Vertical movements on the scales change the display and thus also the acting force.


If the student standing on the scales performs a vertical movement, we can observe changes in the supporting force. Before doing this experiment, however, we should ask the students to draw a force versus time history for a relatively simple case.

For this task we choose a simple bending movement of the legs so that the standing person kneels and crouches. The following line drawing shows the movement again and can be used later to assign it to the force-time curve.

Fig.2 Line drawing of the flexion movement

The students' force versus time drawings should then be categorized and presented to the students for discussion. For example, you can collect arguments for and against certain processes and discuss individual phases. Typical gradients that are drawn by students in such cases are as follows:

Fig. 3 Force-time course of student A

Fig. 4 Force versus time for student B

Course A can be described as four-phase. The representatives of these courses will put forward the following arguments for their course:

1. The course must begin at the level of the weight force (phase 1) and end again at this level after the squat movement (phase 4).

2. The lowering of the body results in a reduction in strength (phase 2).

3. Then the force increases again to the starting level due to the braking (phase 3).

The representatives of the second curve will argue differently with regard to the braking movement in the third point. You will point out that a decelerating movement must rise above the original weight force level in order to achieve a deceleration of the movement. Therefore, in phase 3 this progression went beyond the weight force level.

Following the discussion of the force-time curves, the above statements can now be checked. The purpose of the experiment is to check whether the force in the braking movement rises above the weight force level or remains below it.

Experiment 2: We put a student on the scales and let him flex his knees. So he should go from the upright position to a squatting position.

The following force-time curve results from the observation of the scales, which was recorded with a video camera.

Fig. 5 Example of a force-time curve recorded with a video camera

Note the already eliminated post-oscillations of the balance. It turns out that curve B is obviously the correct one. The argument that higher forces than the weight force are necessary to brake the downward movement proves to be correct. The body shows the greatest downward speed at the moment when the force-time curve reaches the weight force again. In order to slow down this speed, correspondingly high forces above the weight force are necessary.

In analogy to the above movement, we will then consider a standing up movement from the squatting position.

Fig. 6 Getting up from the squatting position

Here, too, the assumptions about the force-time course can be collected first. The following course arises from the experience of the previous example:

Fig. 7 Force-time curve for getting up from the squatting position

Here, too, there is a four-phase course that begins at the weight force level, then rises above it, before it drops below the weight force level and then ends again at the weight force. In the second phase the speed of the body increases, in the third it is reduced again and lowered to zero (phase 4). So we find a similar course in analogy to the downward movement.

We then check this mentally determined force-time curve in an experiment on the scales.

Experiment 3: A student stands up from the squatting position and remains upright on the scales. We will find that the above course is correct and that the analogy to the downward movement is correct.

The evaluation of the video recording will confirm the above assumption about the force-time course.

As a result of these experiments one should try out a few variants with regard to the two movement experiments. Interesting questions arise, for example, from the different implementation of the two movements. How does the force-time course change when the flexion or extension movement is performed relatively quickly or slowly? How do the gradients differ?

In the case of the fast versions, the force-time curves appear naturally compressed over time. The forces show lower (greater relief) and higher values ​​(more braking force), as the following illustration shows for a quick stand-up movement.

Fig. 8 Force-time curve of a quick standing up movement

In the following, we want to deal with two other movements that are used in various sports for performance diagnostics. The first movement is the so-called squat jump (SJ). It is a stretch jump from the static squatting position.

Fig. 9 Squat Jump

Here, too, we consider beforehand what the force-time course could look like before we carry out the experiment. The corresponding proposals are discussed again beforehand and an expectation for the following experiment is formulated from this.

Experiment 4: A student assumes a static squatting position and jumps up from it. Landing should be done next to the scales, if possible, in order not to damage them and to avoid injuries to the feet.

The video evaluation shows the following: The force-time curve initially begins again at the weight force level before it increases sharply with the start of the stretching movement. When you leave the scale, the display falls back to zero.

Fig. 10 Force-time curve of a jump from the squat position (squat jump)

If the landing takes place on the scales again, the force increases sharply at the moment of landing and then reduces to the weight force level.

Two methods can be used to determine the flight altitude. On the one hand, one can determine the height from the force impulse generated during the jump, and on the other hand, it is possible to determine the flight time, i.e. the duration between take-off and landing on the measuring platform.

The impulse is identical to the area under the force-time curve. The larger this area, the higher the take-off speed v and thus also the flight altitude.

F * t = m * v

(Impulse) (impulse)

Of course, our scale measurement is not sufficient for an exact determination of this area, for this you need precise measuring platforms. If you have measured a jump on such a platform, you can either transfer the curve onto graph paper and count the boxes to determine the impulse of force, or you can determine it directly in the computer using a computational method. With the known mass of the jumper, the take-off speed can be calculated and from this again the flight altitude.

The scales cannot be used to determine the flight time either. Using a video recording, however, we can determine the flight time to within 2/100 s (jog shuttle). Anyone who has such an option should take advantage of it. The flight altitude is then determined using the following formula:

h = 1/2 g * (t) 2

(g = 9.81 m / s2; t = flight time in seconds)

The formula used describes the free fall of an object from a certain height. For example, if you drop a stone from a tower, you can calculate the height from which the stone fell by stopping the time until it hit the ground. But since we have an ascending phase and a descending (fall) phase in the stretch jump, the flight time for the jump has to be halved.

h = 1/2 g * (t / 2) 2


t = 0.5 s

h = 9.81 * 0.252 = 0.61 m

Of course, the measurement errors when determining the flight time using a video recording are relatively large, but this procedure is sufficient for a clear illustration of the method. When performing the jumps, make sure that you land with your legs and feet straight after the jump. Only then is it guaranteed that the flight times are not artificially extended.

The second performance diagnostic method that we want to consider is the so-called countermovement jump. This is a jump with a backward movement. It begins with an upright stance, which is followed by a dynamic backward movement. After a movement reversal, the jump takes place upwards.

Fig. 11 Countermovement Jump

Here, too, we collect suggestions on the force-time course. From the knowledge of the previously treated tasks, the pupils should be able to correctly indicate the course. Since this movement is difficult to observe experimentally using the scales, a real, measured course should then be observed. Another interesting feature of this example is the ability to assign individual movement phases to the force-time curve. This task should be solved together using the series of images above.

Fig. 12 Force versus time countermovement jump

First of all, you can see the calm stance on the platform by the parallel course to the time axis, the force is at the level of weight force. With the start of the backward movement, the supporting force drops and the speed increases (phase 1). From the lower reversal point, the increase in speed is reduced (phase 2) and as soon as the curve reaches the weight force, the downward movement is decelerated (phase 3). Only then will the lowest point of the backward movement be reached. At this point in time we find force values ​​that are well above the weight force level.The following stretching movement of the legs generates a further increase in force and ends with the take-off from the plate. The supporting force then drops to zero. The body is only accelerated until the point in time at which the force-time curve reaches the weight force level (phase 4). Below this, the force is no longer sufficient to cause further acceleration (phase 5).

The impulse generated in phase 4 determines the flight altitude. Since a relatively high force value can already be measured at the beginning of phase 4, i.e. the stretching movement, this force is also referred to as the initial force. This initial force can increase the force impulse (the area under the force-time curve) and it is to be expected that higher heights will be reached compared to jumps from the squatting position. The jump movement is shortened by the higher movement speed compared to the squat jump, but the gain in initial strength more than outweighs this small loss of time in which strength can work.

The point in time of the stretching movement cannot be determined directly in the force-time curve. But it can be determined mathematically. To do this, the impulse for phases 1 and 2 must first be determined. Then the point is sought where the area of ​​phase 3 is the same as the sum of phases 1 and 2. Phases 1 and 2 characterize the impulse that is responsible for the downward acceleration and this must be just as large as the impulse to slow down the downward movement (braking impact).

The assignment of the movement to individual movement phases then looks like this:

Fig. 13 Force-time curve and line drawing Countermovement Jump


We have seen that simple movements can be investigated experimentally with regard to their force-time curves even with simple means. After working through the above examples, the students should be able to "think" into force-time courses and interpret them appropriately. Many other examples can be found in sport in which we find phenomena similar to those in the treated ones. For example, all one-legged and two-legged jumps can be differentiated in terms of their recovery (amortization) phases and extension phases. There we repeatedly find typical force-time curves that provide information about the quality of the movement execution. Force-time curves therefore form an essential basis for a quantitative movement analysis.

GÖHNER, U .: Being able to understand force curves. Sportuntericht 1993, 42, 4, 139-147.
GÖHNER, U .: being able to interpret force curves. Sportuntericht 1993, 42, 4, 148-160.
WILLIMCZIK, K. (Ed.): Biomechanics of sports. Reinbek. 1989.