# How to calculate the density of foam required to cushion impacts?

I have a treadmill desk and my downstairs neighbour is complaining about the noise. Specifically the noise made by the impacts of my walking. Unfortunately the floor of my flat is not concrete but made of wooden beams topped with a laminate floor: not a lot of mass to absorb the impacts and not much dampening either. So, I have to do that myself. Ideally I'd have a big slab of marble and a length of open/closed cell foam of just the right density and dimension and would sandwich that underneath the treadmill. I don't have and couldn't carry a big slab of marble, so as a stand-in I'm going with a large wooden board as thick as they come (or can be glued together). Say a kitchen countertop. What I can't figure out is: How dense does the foam need to be?

### Given

• a treadmill with a weight $$m_t = 26\mathrm{kg}$$ that occupies an area $$a = 8555\mathrm{cm^2}$$ ($$59\mathrm{cm} \times 145\mathrm{cm}$$)
• a human with a weight $$m_h = 70\mathrm{kg}$$ walking at a steady speed $$v = 3 \mathrm{km/h}$$ with decent shoes for runners
• a wooden board with the dimensions of the treadmill used to evenly distribute the impacts across the foam
• open or closed cell foam occupying the same area as the board / treadmill

1. Human
3. Board
4. Foam
5. Floor

### Unknowns

I don't know the force of my impacts caused by the walking nor how much the shoes mitigate.

### Resources

Reducing 3D Printer Noise

• Have you got a specific type of foam in mind? Polysterene, PP foams would have different properties and ultimately behaviour at the same density. Mar 3, 2021 at 10:35
• @NMech Good point! No, I don't have any specific type of foam in mind. I don't know a thing about foam materials so I wouldn't know which one would be best for this. Strictly speaking it doesn't even have to be foam. An air mattress might work, too. But to limit the scope of this question I think it's good to stay with one material / family of materials. Mar 3, 2021 at 11:04
• Interesting question. Maybe might try mounting the treadmill on a base that is a sandwitch of a 4x8 plywood board on 4 underinflated mountain bike inner tubes, perhaps repeated, for the low frequency damping, and strapped down with nylon webbing to keep it from falling apart. In addition, on the outside of the plywood, a layer of camping sleep mat or yoga mats might be a material for damping midrange acoustic frequencies Mar 3, 2021 at 16:04

Its more the noise of the entire floor resonating with your jogging rhythm and vibrating as an echobox.

Even if you manage to soften half of the impact by a clever system of plywood and foam you delay the resonance by just a few steps.

Ideally you would need your treadmill in an enclosure on an expensive suspensions system.

• Yes, this is correct. The floor acting as a speaker is the problem. Mar 3, 2021 at 20:57
• And, yes, I might need a lot of foam or a big air mattress or bicycle tires. And maybe a lot of plywood. I might even have to cast a slab of concrete in place. But I fail to see how it would be infeasible. Surely there has to be a way to calculate the necessary spring / dampening force and get some numbers out to know what ballpark of mass and springiness we're talking about. Then we know if it's impossible. Mar 3, 2021 at 21:03
• You probably can't do much about the ~10Hz components (deep bass component from footsteps, and structure vibrations that can be felt, if applicable), but I think you could significantly reduce the 100-1000Hz components before they couple to the floor frame and resonate from there Mar 3, 2021 at 23:58
• i jog endurance. put in 8 to 10 miles daily. my pace which is average is 5 miles per hour. appoximately 2 steps per second. unfortunately this is very close to natural frequency of common residental structures, or a hormonic of it. its really hard to insulate it. Mar 4, 2021 at 0:12

Your proposed arrangement will probably not be ideal.

putting a wooden board between the treadmill and the foam might make the board act as a speaker phone and make the noise more significant (in the room). This will be more evident if the mass of the board is small.

To give you a more intuitive example, think of taking a sheet of metal with certain weight and width (but different thickness) and vibrating it (across the thickness). As the thickness decreases (therefore mass also ) the noise will become much louder. There are some products that you can use for increased damping.