Determining the Factors and Effects of Energy Loss and Fatigue in Kathak Dancers Caused by Chakkars (ELFKC)

Abstract

“Determining the Factors and Effects of Energy Loss and Fatigue in Kathak Dancers Caused by Chakkars” (ELFKC) explores the intersection of computational modeling and classical Indian dance to investigate the metabolic, biomechanical, and physiological demands of chakkars in Kathak, a North Indian classical dance form. Though Kathak is known for its rapid, sustained spinning sequences, limited scientific literature exists analyzing the energy loss and weakened muscular control these movements impose on dancers. This research addresses that gap by proposing a multi-model framework that quantifies and visualizes energy depletion and evaluating control degradation over a series of chakkars. The current position of this study is divided into two primary research questions (RQ1 and RQ2). RQ1 focuses on the relationship between metabolic factors and energy loss using Wolfram Mathematica (MMA). Energy expenditure was modeled using MET-based formulas, and cumulative energy loss over the course of a specified duration was visualized through interactive 3D plots and line graphs. RQ2 looks at how biomechanical and physiological stressors, including fatigue accumulation, torque, and angular momentum, affect dancer stability. This was accomplished using Stella Architect to simulate dynamic system behavior. Both RQs focused on being adaptable to the user through 3 major components: dancer weight, spin rate, and duration of chakkar sequence. The results showed that energy loss increases exponentially beyond certain spin rates and that higher angular momentum and torque, compounded by fatigue accumulation, lead to accelerated loss of stability and control, specifically after 14 to 16 seconds of continuous spinning. However, this could be mitigated by changing posture and exploring different training regimens that focus on active recovery rather than just stylistic elements. This solution can be tested through the third research question (RQ3); however, a limited time frame inhibited the research from moving past RQ2. Even then, this framework, as it is now, can be adapted for other physically demanding performance art forms, supporting future implications in sports science and safety.

Keywords: Energy loss, Kathak, torque, chakkars, MET values, stability, fatigue, angular momentum, calories

Introduction

In the northern Indian state of Uttar Pradesh, over 2000 years ago, storytellers travelled around to tell tales of Hindu gods and goddesses through dances that included rhythmic footwork, hand gestures called mudras, facial expressions, and turns, often done at high speed, called chakkars. This soon evolved into the popular North Indian classical dance form known as Kathak. As one of the most critical parts of the art form, chakkars are a Sanskrit-derived word meaning rounds, referring to the turns Kathak dancers make within their choreography. These balance and precision-dependent movements are integral to the storytelling element Kathak originated from. They also show a dancer’s technical prowess and physical conditioning based on the dancer’s ability to perform multiple of them consecutively without losing form or rhythm. To do this, a great amount of balance, coordination, and muscular control is required. Therefore, the physical demands of chakkars are substantial. Each spin requires activated core muscles for stability, lower limbs for propulsion and balance, and peripheral awareness for preventing dizziness (Dupont 2021). As time passes, the repetitive nature of these turns without proper rest and conditioning can cause fatigue, leading to decreased control, a compromised technique, and a higher risk of injury (Kulshreshta). This can be attributed to an array of physiological and biomechanical factors (Abbiss). For example, the sustained spinning tires the body faster because of the constant use of the lower limbs, impacting the joints and muscles which are important for staying balanced during the rotations (Błażkiewicz).  This can also lead to musculoskeletal pain in dancers, emphasizing the need for better energy management (Karde). Studies of Kathak dancers also show that heart rate and lactate levels are affected by recovery, and the additional mental strain can make it harder to stay focused (Schiphof-Godart).

By taking into account the impact chakkars have on a dancer’s stability and endurance, this study explores this relationship between rapid energy consumption and a Kathak dancer’s lack of steadiness. Specifically, the integration of concepts from biomechanics, metabolic energy use, and dance physiology can play a part in determining the prime number of spins a dance can sustain before reaching harmful levels of energy loss, compromising stability (Chopra). 

Reviewing past literature and research on this topic helps to identify information that has gaps and can be built upon. Unfortunately, the science on the chakkars or any dance spins in general can be obscure. So, this study combines the data for dance turns in general and implements them into the role of Kathak, as they share the same characteristics when it comes to energy loss and recovery from fatigue. 

According to various articles, energy expenditure correlates to Metabolic Equivalent of Task (MET) values, which are commonly used to quantify energy expenditure in physical activities by providing the ratio of an activity's energy cost to the resting metabolic rate: 1 MET is equivalent to the energy used at rest (Jette et al.). This ratio allows researchers to estimate caloric burn of intensive, endurance-based activities without requiring newly tested data, making it a valuable tool for analyzing chakkar movements in Kathak. Though general MET values for dance exist in the moderate to high range, true values of the calories burned per spin would depend on factors like body weight, the duration of the spin, and movement intensity (Chopra et al. 2023). The optimal number of spins a dancer can sustain before their performance is compromised can be determined by understanding that energy depletion caused by this process of caloric loss leads to physical fatigue, impaired neuromuscular control, and decreased stability and coordination (Abbiss and Laursen 2005).

Moreover, biomechanical principles—angular momentum, torque, and balance—can affect a dancer’s stability. Angular momentum depends on rotational inertia and velocity to help maintain continuous motion. Torque, on the other hand, controls acceleration and deceleration based on the amount of muscle force being produced. Balance also utilizes the muscular system as well as the nervous system to counteract destabilizing factors while spinning (Błażkiewicz 2021). Because of this, joint stress and muscle fatigue play an important role in a dancer's ability to sustain repeated spin as high rotational speeds can increase the dependency on hip and leg muscles. This can lead to strain and fatigue, compromising postural stability (Dupont 2021). Studies on pirouettes (turns in ballet that require a lot of energy, making it comparable to Kathak chakkars) have shown that joint loads are unevenly distributed: higher levels of stress are placed on the weight-bearing limbs, like the leg, which can increase the risk of injuries caused by overusing particular muscles (Błażkiewicz 2021). By understanding these forces, this study can aid in optimizing technique and minimizing injury risk for dancers performing sustained rotations.

Lastly, recovery methods, though hard to quantify and difficult to research, can be modeled by investigating the body's recovery processes, muscle repair, and endurance adaptation. As already stated, the high-intensity movement of chakkars can lead to neuromuscular fatigue, impacting motor stability and coordination. Fatigue in these endurance activities results from both central and peripheral factors (Abbiss and Laursen 2005). Central refers to the neurological system, as it is the main system affected by fatigue, and peripheral refers to the muscular system because it is the reason for the fatigue. For dancers, this means an effect on postural control and the increased risk of instability in repeated movement (Dupont 2021). Recovery plays a crucial role in performance optimization since active recovery, like low-intensity movement, can facilitate lactate clearance and muscle recuperation (Chopra et al. 2023). Existing comparisons between active and passive recovery methods suggest that structured cooldowns can improve endurance and delay fatigue in dancers (Chopra et al. 2023). Case studies on physical conditioning in Indian classical dancers have also shown that strength training and targeted flexibility exercises can improve overall endurance, thus reducing the risk of injury as needed (Kulshreshta et al. 2022). By understanding these recovery mechanisms, a direct solution can be provided to develop strategies that help a dancer sustain performance and prevent long-term musculoskeletal issues. Not only Kathak dancers, but also other dancers or athletes of endurance-based sports that involve prolonged spinning, like figure skating, can benefit from the results of the study (Nair). 

Understanding existing research and acknowledging room for further investigation of this topic formulates the question: “What are the main factors and their effects on energy loss and fatigue in Kathak dancers, specifically caused by chakkars?” For the sake of this study, this question is broken down into three parts, called RQ1 (biochemical viewpoint), RQ2 (biophysical viewpoint), and RQ3 (recovery), all of which are broken down into 3 subparts to ensure a cohesive analysis of the question:

• RQ1. How does energy consumption from chakkars influence a dancer’s ability to withstand those spins before fatigue leads to instability?

  • Graph the impact of spin characteristics on energy depletion rate 

  • Create a model for cumulative energy loss over multiple chakkars 

  • Analyze models to identify the maximum number of chakkars

• RQ2. How do biomechanical forces, such as angular momentum and joint stress, influence stability and endurance in Kathak chakkars?

  • Simulate the impact of physics-based factors on stability

  • Integrate biomechanical factors and equations into the model

  • Assess how these factors and spin characteristics reduce dancer control

• RQ3. How can different recovery methods affect the long-term performance of a dancer and prevent injury?

  • Compare active vs. passive recovery using caloric recovery data

  • Show how biochemical mechanisms affect long-term fatigue and recovery

  • Examine the result of various cooldown methods on continuous chakkars

Unfortunately, the limited time for the study allowed for only RQ1 and RQ2 to be addressed. Nonetheless, they provide a smooth transition into RQ3 if this study is continued further into the future.

Methods 

As stated in the previous section, the primary research question for this study was broken down into three parts: RQ1, RQ2, and RQ3. Overall, this study was mainly theoretical, utilizing estimated numbers, based on research from previous related literature, for various components of the computation approach that may be replaced with experimental data found in later studies. Other values like body weight and spin rate were dependent on a scenario of a piece performed by a 61 kg dancer that ended with 18 seconds of continuous 12 high-speed turns followed by 21 moderate-speed turns. However, the experiment is set up for users to modify the code to fit their needs properly, similar to the editing ability of the research-based data. Because only RQ1 and RQ2 were accomplished in the study, as RQ3 required greater resources, this section is broken down into how the first two parts were studied. 

When going about modeling the metabolic energy loss using Wolfram Mathematica Version 14.1 (MMA), the Metabolic Equivalent of Task (MET) needs to be determined. For this experiment, it was assumed that the MET value would be set at 7.0 because other sports that depended upon moderate to high intensity spinning, like figure skating and ballet, were similarly ranked (Jette et al). The spin rate was determined by dividing the number of turns by seconds, which simplified into 11/6 or 1.8 spins per second. These values were used to approximate chakkar frequency. The user-dependent data was then imputed within the MET formula (MET weight 3.5/200/60) (Jette et al). In this equation, one MET is ~3.5 milliliters (mL) of oxygen consumed per kilogram of body weight per second (the original 1 minute was converted to 60 seconds), helping individuals estimate the amount of oxygen used by the body, which is directly tied to the intensity of the activity. Next, a chain of conversions were implemented, starting with the time per spin. It was determined by taking the inverse of the spin rate and integrated into a later equation that measured kcal per spin. This new value was then multiplied by the number of spins done over the full sequence of chakkars (the product of the duration of the particular section and the rate of each spin). The final value gives the total energy lost over the complete chakkar sequence as shown in Figure 1 below.

Figure 1. Calculations determining the total energy loss over a specific period of time

This specific product showed the sub-calculations to find the total amount of energy lost. However, a more user-friendly product was created using the “manipulate” command on MMA. It was based on similar data but allowed users to customize their weight in kilograms, their spin rate in spins per second, and the duration of the chakkars in seconds through the use of sliders. An example of how this tool looks is shown in Figure 2 below.

Figure 2. User-friendly tool to determine total energy loss}

To help visualize the energy loss per spin in relation to the spin rate and the dancer’s body weight, a 3D plot was created in MMA, which can be seen below in Figure 3.

Figure 3. Correlation between body weight, spin rate, and energy loss}

In order to accomplish the last requirement for RQ1 to be answered, the maximum number of spins for a dancer in this situation needed to be determined based on a set threshold created in MMA. By creating a fatigue model inspired by the cumulative energy loss model, in which the Table and ListLinePlot functions were used, integrated within the first two parts of RQ1, a nonlinear energy cost increase occurred at around 20 seconds which corroborates research by Abbiss and Lauren (2005), who determined that fatigue reduces efficiency exponentially. In addition to the fatigue model, an estimated threshold graph was created based on data by Jette et al. (1990), stating that a dancer’s estimated aerobic max output is often around 10 to 12 METs. This plot is shown in Figure 7 in the following section where it will be further explained.

With RQ1 completed, RQ2 first required confirmation of the effect various physics-based factors had on stability. To do this, the Plot function was used between angular momentum and spin rate, ranging from 0.5 to 3 spins per second. Before this though, inertia and angular velocity based on spin rate must first be determined in order to find the angular momentum (I*w). 

The basic chakkar technique of Kathak dancers from the Lucknow Gharana, a stylistic family of Kathak, consists of two positions accomplished over the course of each turn (Dewari). The dancer starts by extending their arms at shoulder-level and rapidly closing them, when they face the back, to where their fingertips point towards each other without crossing the sternum. This is known as utpatti. Figure 4 shows a diagram that appears in a paper by Dewari, Bogin, and Chandel (Dewari). For the sake of this calculation, posture A will be regarded as the tight position and posture B will be regarded as the extended posture (Journal of Sports Science & Medicine).

Figure 4. Diagram of the two positions analyzed

To find the moment of inertia for this experiment (mass*r²), a set radius is needed. In the hypothetical situation of the 61-kg dancer, it can be assumed that the distance between their elbow and their sternum at the tight position is 0.3 meters and the distance between the edge of their fingertips and their sternum at the extended position is 0.76 meters. So, these values were used for each line on the plot. The angular velocity utilizes the spin rate (1.8 in this case) in its equation s/rt. Because spin rate is being accounted for what is essentially length of the arc over time or s/t, the equation can be modified to 2*pi*spin rate. 

After the plot was created on MMA, a systems dynamic was set up on STELLA Architect (STELLA). Two primary stocks were created: one to model fatigue and the other to model stability. To show fatigue accumulation, an inflow was connected to the fatigue stock from a cloud, and to show control degradation, an outflow from the stability stock was created to demonstrate control degradation. Additional converters within the model include fatigue rate (connected to fatigue accumulation inflow), torque (connected to fatigue accumulation inflow and control degradation outflow), and angular momentum (connected to fatigue accumulation inflow and control degradation outflow). The fatigue stock was also connected to the torque and the control degradation outflow directly. This dynamic is shown in Figure 5 below. 

Figure 5. The flow of energy between various stocks and converters}

Within the diagram, fatigue started off as a value of 0, assuming the dancer has not been performing an earlier part of the piece, and stability started at 100 to assume complete stability as a dancer is standing straight. The inflow of fatigue accumulation was determined by multiplying the rate of fatigue by the quotient of the angular momentum divided by torque. The fatigue rate was estimated to be about 0.3 based on previous literature that implied Kathak chakkars are often on the lower side of high-intensity activity (Chopra). To find the angular momentum, a similar technique to the one used for Figure 4 is employed in MMA, except only one radius measurement is allowed. In this case, the hypothetical dancer is performing the chakkars using a different style that consists of staying at utpatti (the tight position) throughout the chakkar with no extension of the arms; therefore, the radius can be assumed to be 0.3 meters. Using this set radius, the code shown in Figure 6 helped determine the angular momentum in this particular situation, which was then imported into the angular momentum converter in STELLA. 

Figure 6. Code for finding the angular momentum

Torque was estimated using reasoning from literature, existing data, and mathematical calculations. In the model, its regular formula (I*a) was multiplied by the difference of the fatigue stock from 1. This assisted in modeling the reduction of torque as fatigue increased, effectively scaling the values (Blazkiewicz). To determine torque, it was assumed that the dancer reached full spin speed in 0.5 seconds and that the final angular velocity was equal to 2 pi multiplied by the spin rate. With the velocity being equivalent to 11.5 radians per second, it was divided by change in time (0.5 seconds) to provide a quote of 23 radians per second squared for angular acceleration. This was multiplied by the moment of inertia determined in the MMA code earlier, giving a total of about 28.1 newtons times meters. By using this line of reasoning, the idea that torque and control have a direct relationship is confirmed (Nair). Lastly, the control degradation was modeled by relationships between the factors: as torque decreased and angular momentum increased, fatigue increased and control was lost substantially (Blazkiewicz). Hence, the angular momentum was in the numerator and torque was in the denominator. Because control degradation is an outflow, fatigue was kept on the numerator as the flow was already set to be “negative.” This simulation was then set to run from 0 to 18 seconds to observe changes in fatigue and stability over that amount of time, effectively accomplishing the final two parts of RQ2. 

Results

After creating the user-friendly tool in MMA for part of RQ1, a plot was created to help determine the maximum number of spins the hypothetical dancer would be able to complete before their fatigue started to affect their stability. In Figure 7, the graph is shown with the red line demonstrating the fatigue curve and the dotted blue line representing the threshold from 0 to 30 seconds. 

Figure 7. Threshold for maximum number of spins with a set spin rate

On the graph, there is a clear section in the beginning, from x=0 to x=11, where the linear threshold has y-values above the exponential fatigue. For these values, the dancer’s fatigue is not significant enough to be noticed. Using the SelectFirst and Transpose function on MMA, it can be calculated that the lines intersect at 11 seconds, where the fatigue curve passes the threshold. Multiplying 11 seconds by the spin rate of 11/6 helps determine the number of spins accomplished within the first 11 seconds: about 20 chakkars. This answers the question from RQ1 that asked what the maximum number of chakkars that can be accomplished before fatigue becomes significant enough to affect a dancer’s performance. Though the answer is not universal, the model created based on past literature and existing formulas can assist to find a solid estimate for users. With some values being reliant on the user’s situation, the model also allows for personalization and more reliant data. 

The next MMA model was for RQ2’s comparison of angular momentum based on the physics of a dancer's posture. The graph plotting the line for both the tight and the extended posture is shown below in Figure 8 with the orange line showing posture A and the blue line showing the extended posture.

Figure 8. Visual representation of the change in stability based on dancer posture

This graph holds significance for newer dancers because as they learn more advanced, stylistic elements that require quicker spins, they are often encouraged to keep the tight position throughout the turn rather than starting with an extended one. Often, the implied reasoning is that it helps with stability. To know if this is true, the relationship between angular momentum and stability must be understood. In this case, a higher angular momentum requires a greater force in kilograms times meter squared per second which can be harder to control, leading to less stable chakkars. Therefore, if the angular momentum of the extended posture is greater than that of the tight posture, the implication can be proven true, and it does as shown in Figure 8. 

The last product for RQ2 was graphed simulation data created by STELLA. The graphs produced determined the trend and correlation between varying levels of fatigue, control, and stability. For a better comparison, control degradation and fatigue was plotted on one graph while stability was on a separate graph. This choice was made to fix errors in the scaling of the plots. Because stability has significantly greater y values than control and fatigue do, a separate graph for stability is needed in order to not warp the y values to a point that the levels of control and fatigue cannot be properly shown. Both the graphs are shown in Figure 9 below.

Figure 9. Correlation between fatigue, control, and stability

These graphs validated that fatigue increases and stability decreases under high torque and angular momentum conditions (or, more simply, rigorous activities). They also showed downward trends in the stability stock as indicators of compromised neuromuscular control. Quantifiably, at around 11 seconds, the line for control degradation and fatigue starts to have a more extreme rate of change, and at 15 to 16 seconds there is a steep decline in stability and a steep incline in control degradation. This connects to and further supports the metabolic threshold measured in the end of RQ1 that found 11 seconds to be where fatigue started to impact control and stability. These graphs also provided a basis for RQ3 if it were to be studied because they showed a high fatigue accumulation if the spin rate was increased, suggesting that a higher fatigue accumulation can be achieved with a reduced recovery time between or before the spins. 

Discussion

ELFKC computationally explores how Kathak chakkars impact a dancer's energy expenditure and control. The analysis suggests that prolonged or rapid spinning sequences cause measurable energy loss and stability decline, with performance thresholds identifiable through combined biomechanical and physiological modeling. Wolfram Mathematica enables precise calculations of metabolic output, while Stella Architect runs dynamic simulations of fatigue accumulation and control degradation. Together, these tools can provide a holistic understanding of the physical costs associated with chakkars in Kathak dance, reinforcing the value of interdisciplinary methods in analyzing traditional art forms.

While RQ1 and RQ2 were addressed through detailed modeling of energy depletion and biomechanical control loss, RQ3 (the assessment of the neurological and proprioceptive aspects of spin stability) remains unexplored due to time constraints. Future work could incorporate neurological feedback systems, sensory processing, and muscle activation response to better reflect the internal physiological adaptations dancers rely on for balance and recovery. If greater access to advanced technology were available, experimental data could be validated using motion capture or wearable biometric sensors, giving feedback that could enhance the models’ calculations and simulations. Overall, this project offers a strong foundation for understanding the science behind classical dance through the use of computational tools, supporting dancer health and performance through evidence-based information.

Acknowledgements

The author thanks the Department of Science at the North Carolina School of Science and Math (Durham, NC) for the opportunity to study computational science. Special thanks is given to the Journal of Sports Science and Medicine for providing standard sports medicine information and pathways to other studies in the same field.

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