There’s more to an exercise ball than you thought


Anyone who has ever been to the gym has most likely seen or used an exercise ball. They’re big, inflatable balls that many people use to help them facilitate exercise or to stretch. They’re good for strengthening your core and improving your balance. Incorporating an exercise ball into your daily workout will add a challenge to your routine. A lot of people may also use them at home due to the fact that they are very affordable and versatile. While they may seem harmless, there can be serious risks when using one. It is important to use the correct size ball based on your height in order to get the most effective workout. It has to be inflated properly in order to work correctly. An over or under inflated exercise ball will put you at a greater risk for injury. The biggest danger of an exercise ball is having it burst. Over-inflation, improper use, and excessive user weight are some common ways that the ball may burst. The first step in preventing an exercise ball from bursting is choosing the right material. The material needs to be able to support the user and keep the integrity of the ball. Some common materials are vinyl and plastic. It’s important to figure out the force that is being applied to the ball, in order to figure out the strength of the material needed. The material needs to have a high tensile strength to support the user and prevent the ball from bursting and injuring the user.

Example of Exercise Ball



The first step is figuring out the appropriate size of the ball based on height. When sitting on the ball, your knees should be at a right angle and your thighs should be parallel to the ground. The average woman in the United States according to the CDC is 64 inches tall and 166 lbs (75.3 Kg). According to anthropometric dimensional data, the ground to her knees is .285 (Anthropometric data-197t3u3) of her height.

.285 * 64 inches = 18.24 inches

Proper size for an exercise ball based on height


This means that the proper exercise ball should be 18 inches in diameter or 46 centimeters.

To find the best material, we can calculate Young’s modulus based on Hooke’s Law. 


Hooke’s Law  

?= stress = Force/Area

E= Young’s modulus

ɛ= strain= Δl/l

Surface Area of Sphere = 4 * π * r^2


  • Exercise ball undergoes elastic and linear response to force
  • All of the users weight is being applied over the top half of the ball
  • Assume the exercise ball displaces 1 inch when force is applied


?= Force/Area

Force = 75.3 Kg * 9.8 m/s^2 = 738 Newtons

Half the area of sphere = ½ * 4 * π * 9.12^2= 523 in^2 = .337 m^2

? = 738 N / .337 m^2 = 2190 N/m^2

ɛ= strain= Δl/l

Ɛ = 1 inch/18.24 inch = .0548


2190 N/m^2 = E * .0548

Young’s modulus: E = 4.00 x 10^4 Pa


From this calculation, an exercise ball would need to be made of a plastic or vinyl with a Young’s modulus of around 4.00 x 10^4 Pa.

The assumption that the user’s total weight is distributed on the entire top half of the exercise ball led to the Young’s modulus to be underestimated. In real life, the user’s full weight wouldn’t be on the ball and it would also be distributed over a smaller surface area. The actual material would have a higher Young’s modulus than the calculated value. 


Learn more about the things you can do with an exercise ball!

Exercise Balls – The Ultimate Guide


No Pain, No Gain

From the average gym goer to professional athletes, anyone can experience delayed onset muscle soreness, or DOMS. It strikes 24 to 72 hours after a period of reduced activity or when introduced to new exercises. The symptoms range from mild muscle tenderness to debilittating pain. If you’ve ever experienced this, you know the struggle of walking up and down the stairs and putting on pants in the morning. Your muscles feel stiff and are sore to the touch. To understand the types of activities that cause more severe and frequent soreness you need to know the different types of muscle contractions. There are isotonic contractions which generate force by changing the length of the muscle and isometric contractions which generate force without changing the length of the muscle. The two different types of isotonic contractions are concentric and eccentric contractions. Concentric contractions cause the muscle to shorten and generate force whereas eccentric contractions cause the muscle to elongate in response to a greater opposing force. Eccentric activities create the most intense soreness because they induce micro-injury more frequently than any other type of contraction.

Figure 1: Eccentric contraction

Many people look to the internet for ways to prevent and reduce the symptoms of their soreness. Some common ways people prevent soreness is by performing a cardio-based warm up or static stretching. Once the soreness kicks in, common ways people reduce their symptoms are non-steroidal anti-inflammatory drugs, massaging, cryotherapy, stretching, homeopathy, ultrasound, and electrical current modalities. Without any background knowledge, people might be wasting their time trying techniques that have no proven evidence of preventing or reducing soreness. What really is the best treatment to alleviate the symptoms of DOMS or is time your only option?

One study looked at the effects of stretching before and after exercise on muscle soreness. They did a systematic review of five different studies which all included young healthy adults as their participants. The participants stretched from 300 to 600 seconds between the studies and muscle soreness was measured at 24, 42, and 72 hours after exercise. They found that stretching before or after exercise has no effect on delayed onset muscle soreness.

Another study was performed that looked at if a warm-up or cool-down reduces delayed onset muscle soreness. They randomly assigned 52 healthy adults to four groups: a warm-up and cool-down group, a warm-up only group, a cool-down only group, and neither warm-up nor cool-down group. The warm-up and cool-down was 10 minutes of walking and the eccentric exercise was 30 minutes of walking backwards downhill on a treadmill inclined at 13 degrees at 35 steps per minute. The participants were asked to record their muscle soreness 10 minutes after exercise as well as 24, 48, and 72 hours after. The results showed that a cool-down had no effect on soreness and a warm-up produces a small reduction in muscle soreness.

It’s a day after your hard workout and you can’t walk. What do you do? A study in Sports Medicine found that cryotherapy, stretching, homeopathy, ultrasound, and electrical current modalities all have no effect on DOMS. They found that massage could have an effect based on the timing of the massage and the technique used. This data was also supported by a study done by Nicole Nelson, who found massages to be a promising result in reducing soreness.

While there are a lot of studies done on DOMS, there are several limiatinos. One problem is that there are multiple ways to measure muscle soreness, so it can be hard to compare studies to each other. Some studies used a visual analogue scale and some used a 0-10 measurement. The mechanism for what causes delayed onset muscle soreness is still unknown, which makes it difficult to prescribe an accurate treatment. In one study, walking was the warm-up as well as the exercise to induce the muscle soreness. They didn’t look at if having a walking warm-up would still be effective if squats was the exercise inducing the muscle soreness. For some of the studies, the outcome measures were all self-reports so the participants could have mis-reported.

From my own personal experience, I experience delayed onset muscle soreness whenever I try out a new workout or increase the intensity of an old one. Usually, I just let the soreness runs its course and don’t do anything to reduce the symptoms. From the literature, it seems like the best thing to do is wait. To prevent DOMS you can try and ease into the exercise rather than performing it at full intensity the first time. Cryotherapy, stretching, homeopathy, ultrasound, and electrical current modalities all had no effect on muscle soreness. Warming up before exercise seemed to have a small effect, but won’t drastically reduce the severity of DOMS. There still needs to be a lot of research done on the mechanism of DOMS in order to find out the appropriate treatment.

Questions and Comments

Are there any other methods of prevention or treatment that work for you?

Have you tried any of the treatment options above and have they helped alleviate your soreness?

Please leave any comments or questions about DOMS below!


Recommended Further Reading

No Pain, No Gain? Five Myths About Muscle Soreness 


walking through the sky

Seating and treadmill exercise device

Patent Number: US7052441 B2

Patent Filing Date: Jan 23, 2004

Patent Issue date: May 30, 2006

How long it took for patent to issue: 2 years

Inventors: Mithra M. K. V. Sankrithi

Assignee: The Boeing Company

U.S. Classification: 482/54

Claims: 12

If you’ve ever been on a long distance flight you know the feeling of sitting upright for countless hours, not being able to stretch your legs. You try and walk up and down the aisle, but between flight attendants handing out food and drinks, passengers waiting in line for the lavatory, and people making conversation it makes it difficult to efficiently stretch your legs. What if you could take a ten-minute walk while 36,000 feet in the sky? This patent proposes to create a seating and treadmill exercise device for aircrafts that would allow passengers to stretch their legs and partake in low impact aerobic exercise as well as a safe seat for the flight attendants.

There were 12 claims outlining the assembly and main components of the device. The seating and treadmill exercise device would be capable of being in a stowed or deployed position. While stowed, passengers would be able to board and exit the aircraft as well as create extra space in the cabin. A folding chair would be secured to the backside of the treadmill in order for a flight attendant to be safely seated during take off and landing. The folding chair will be capable of moving from the folded to unfolded positions as well as being wide enough to seat two flight attendants. While in flight, the treadmill can be in the deployed position for passengers to use. The treadmill will have on-off controls, speed controls, and a safety handrail. To go from the stowed to deployed position and vice versa, the seating and treadmill exercise device will be rotated about an axis and secured to an interior wall by a securing device such as a latch, clamp, hook, or belt. This device will allow passengers to easily exercise and stretch their legs, as well as maximize cabin space.

Figure 1: Device in stowed position

Figure 2: Device in deployed position

The treadmill will work like a typical treadmill you would find at your local gym. There will be a motor to drive the endless belt and its rollers. A possible motor would be a 2.5 horsepower DC motor that operates at 18 amps, 6700 rpm, and 130 VDC. This device is different from previous devices because it is meant for an airplane and doubles as a seat! There have previously been folding treadmills, but not one with a chair attached to it that can be used in the sky.

I think this a great idea that would benefit passengers who need a little bit of an extra stretch. Anyone on a long distance flight that wants to get his or her legs moving, and take a break from their seat would definitely use this device. This would especially benefit passengers who are at risk for DVT (deep vein thrombosis), because walking and stretching their legs would allow for increased blood flow.

Being someone who has been on a lot of international flights, I would definitely use this machine. After the first 5 hours of being on a flight my legs start to cramp, my back starts to hurt, and I get restless. If I were able to take a ten-minute walk mid flight, it would relieve the pain in my back and get the blood flowing in my legs again. It’s a great way to get passengers moving while 36,000 feet in the sky.

You can view the full patent here!