The Physics of a Supportive Bra Explained

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To all boob owners reading this: I would like you to take off the clothes on your upper half and stand in front of a mirror. I would buy you dinner first, but unfortunately on my student budget I can't afford to wine and dine all of my readers, so you'll just have to take a chance on me. 

If your body shape and ability allows, I would like you to use your hands to support and mould your boob into the ideal shape you would like them to be in a supportive bra. Usually, people are looking for a bra to give them the following sort of profile:

Side profiles of some unsupported and supported breasts

If you've gone and moulded your boobs, I'll wager you have done something like I did to achieve that look.

You've positioned one or both of your hands in such a way that it both lifts your boobs but also pushes them in to your chest to give them that lifted but also rounded appearance. And since this is what you would like a bra to do, this is what an ideal, well-fitting bra is going to do.

You may have also gathered them in from the sides for a narrower silhouette, pushed them together for cleavage or pushed them to the sides to minimise them. While having a big impact on appearance, these side-to-side movements aren't covered in this post, which focuses only on the lifting and rounding of boobs. If you want a different shape (such as a very flattened chest), it's likely that a standard bra is not going to do that job well. 

You can put your top back on now.

So a bra needs to use the cups to lift the boobs and push them in. To do this the edges of the cups need to be held firmly against the torso to keep them in position - otherwise you're trying to build a supportive garment on an improper foundation.

This means that for a truly supportive bra we need to establish how it will fit. In an underwired bra, the wires should sit around the breast tissue at the root such that:

a) the wires are firm against the body, and not floating in the centre or sitting on breast tissue

b) the wires hug the root of your breast (the area where your breast tissue attaches to your chest), with minimal space between the breast and the bra 

A bra with a good foundation

A bra where the wires float at the centre front, sit on soft and moveable breast tissue at the front or side, or allow the breast tissue to fold at the inframammary fold or the cleavage will lack in support. This is unfortunately very common, however, and is something I call a boob hat. Boob hats are a major cause of bra related pain and dissatisfaction.

 

A "boob hat" has a poor foundatin

Additionally, a bra where the breast is lifted but the wires are too wide or sit too low is also not ideal as this allows the breast to move within the bra. This can occur with bras that have been sized up for depth, parachute bras or in homemade bras, a wire size that is too large.

A too large underwire also causes a poor foundation

What forces do your boobs put on your bra?

I'm sure you've heard of Newton's Third Law - every action has an equal and opposite reaction. What this basically means is when you lift your boobs upwards and push them inwards with a bra, your boobs push outwards and downwards on the bra. This force is distributed over the bra cups and looks something like this: 

It's clear that we need a simpler model to describe the forces in a way that's easy to understand and gets the most important information across. A model I've seen a couple of times before describes bras as having a cantilever support system. While that's not untrue at a basic level, I feel the shape is too abstracted from a bra and unfamiliar enough to most people to a) be easy to understand and b) apply well enough that we can learn things from it.   

For now, let's concentrate the forces the boobs put on the bra at the nipple, to make them easier to analyse. We will also only consider external forces for now - i.e. how the bra as a whole works as a support device. In the extended version of this post, we will consider a simple 2D shape representing the structure of a bra, so we can discuss the distribution of forces a bit more in depth, so check that out if you're interested.

How is the bra resisting those forces?

The three main rules of force analysis on a 2D static object are as follows:

1. All forces can be split up into their vertical and horizontal components, which we can consider as separate forces. 

Splitting a force into its components

2. All vertical forces on a point must be balanced (add up to 0), and all horizontal forces must be balanced (add up to 0).

The horizontal components and vertical components are balanced, the object is stable

 

3. All moments about a point must be balanced (add up to 0).

We will focus on 1-2 now - for discussion on 3 you can read the extended version of this post on Ko-fi.

Overall force balancing in a bra

We have these downwards and outwards forces that need to be balanced. For simplicity, we'll consider them all acting at one point. Because we can consider the vertical and horizonal components separately, let's split this single force into its components and consider these two forces separately.

The force caused by the breasts has been concentrated and split into the weight of the bust and the outwards force of the bust

 

1. Outwards force of the breast

This is fairly simple: the tension on the band directly opposes the outwards force, bringing it around to your back. 

2. Downwards force of the breast (the breast weight)

Your immediate thought might be using the straps to create the upwards force - and they do to a degree, but if you rely entirely on the straps that's a lot of weight to put on two small strips on your shoulders. The real heavy lifter (harhar) in this situation is the band. 

But wait, the band goes horizontally? Yes, it does, but have you ever worn a belt to keep your trousers up? It's the same principle. Friction is the force that resists motion, so friction between the band and your body will stop it sliding downwards. The friction is caused by the band gripping into your skin, but how much friction can a band provide?

To understand friction we first have to understand a concept called the Normal Force. The normal force is the perpendicular force caused by an object in contact with another object - such as the force that the ground puts on you when you stand on it. The friction that any surface can provide is directly proportional to this normal force.

The normal force, in this case, is the ground counteracting your weight to stop you falling into the earth!  If someone tries to push you, the friction that stops you sliding along the ground is proportional to that normal force caused by the ground rudely being in the way of your fall.

 

And so, when you put a snug, elastic band around yourself, the band wants to contract to stop being stretched out, but your ribs are in the way - putting a normal force on the band.

Your rib cage resists the tension of the band, this resistance is called a normal force

This normal force causes friction, opposing the downwards movement of the band, allowing the bra to resist your bust weight instead of sliding down! Neat!

What's this about moments?

A moment is what's created when you apply a force at a distance to a point, the moment being equal to the force * distance. Like applying a force to turn a spanner (wrench for Americans) moments cause objects to rotate. However...

This post is already quite long, and the stuff about moments is not necessary for basic understanding and a bit harder to teach. While I was writing this I realised that the moments are really the cherry on top of a pretty descriptive system. I decided to remove this section from my post and instead have added the complete version to my Ko-fi, which you can read for £2. 

Does this mean the straps are unimportant?

No, not at all. The job of the straps is keeping the fabric of the cup - especially the upper cup -  taut, so the cup fabric itself can resist the outwards and downwards motion of the breasts, with the cup fabric being built upon the solid foundation of the wires, band, and straps. Strapless bras are very difficult to design for this reason, and this is why most strapless bras you see have tall wires at the side and are  made out of rigid foam, and may feature internal cup boning.

 

So while straps are very important in the fit of a supportive bra, boob hoisters they are not, so if your wires are sitting low below your breast roots, messing around with the straps is not going to fix that problem.

 What can we learn from this?

Part 2 is out, and focuses on how we can integrate these ideas into bra shopping and making with a focus on the band. More to come for the other bra components.

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Afterword

I'll admit to it: this post was largely inspired by a class in the Great Bra Sewing Bee 2021 called The Science of Breast Support. The class focused on 3 main topics: a force analysis of bras, that breast motion can be modelled as a certain type of non-newtonian fluid, and a discussion about stretch fabrics. I took major issues with the first two of those. I may explain my problems with the non-newtonian stuff in more detail at a later stage, but the force analysis is what I will focus on here: I thought the force analysis given in the class was confusing and incorrect at mutiple key points, displaying a fundamental misunderstanding of force summation and some other basic concepts. As someone who cares a lot about science communication it made me very frustrated, so I thought I'd try my hand at an explanation that I believe to be much more accurate.

This explanation also uses fewer specific engineering terms and instead focuses on explaining the concepts behind them, so hopefully it is accessible for everyone who's interested.