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Obviously it's a silly idea. Apart from the cost, it's far too dense and not stiff enough to be a good frame material.

What I'm asking is would it be possible to make a ridable bike from gold? What calculations would be needed to work out what tube size/thickness would be needed?

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What's the point? – Carel Jul 15 '14 at 19:17
You should only ask practical, answerable questions based on actual problems that you face. Chatty, open-ended questions diminish the usefulness of our site and push other questions off the front page. And you are asking an open-ended, hypothetical question: “What if ______ happened?” How is this considered on topic (And worse, upvoted?) – JohnP Jul 16 '14 at 22:00
@JohnP Moderator hat off... I think the "spirit of the law" is more important than the "letter of the law" here. It may not be a problem that the OP actually faces, or an incredibly practical one, but it is clearly an answerable one. I also don't see how it's open ended. Either it can be done, or it can't. The answers have also served to illustrate a lot of frame material properties that are considerations in the making of any frame in any material. My vote is to leave open. Moderator hat back on. But, of course, it's up to the community. If it gets five close votes, I won't reopen it. – jimirings Jul 16 '14 at 22:56
I recently learned how to temper chocolate (so that it sets hard). Maybe I could make a frame out of chocolate. If it doesn't work I could eat it. And it wouldn't be as expensive as gold :-) – andy256 Jul 17 '14 at 1:16
I'm voting to close this question as off-topic because its not question that addresses a real problem – mattnz Feb 2 at 23:10
up vote 7 down vote accepted

Trivially: yes, of course you can. You almost certainly won't be able to ride that bike, though.

The problem is not the weight of the frame, it's the weight of the rider compared to the strength of the gold. Essentially you have an 80kg rider on a frame that might weigh 20kg if made of gold rather than 5kg in steel. The dominant mass is still the rider.

The problem is that the maths is complex and I'm not a mechanical engineer. Broadly, we need to find the yield force at which each key component breaks, and that's determined by how the gold is formed, the temperature, the rate of change of the force and a few other factors. So you can't just say "shear modulus 27GPa" and move on.

To make a bike frame you'd want to quench the casting to harden the metal as much as you can, which would help, but it would still be weak. I am not certain that quenching works on gold. I suspect the main issue would be the dropouts, and you'd need to use long, fat axles - like the 14mm thick axles used on some load bikes - to spread the load and stop the axle just cutting straight through the frame when the rider sat on the bike. Likewise, big, low-pressure tyres to reduce peak forces on the frame.

As you make the "tubes" (probably solid, for practicality of construction) fatter you'll start to run into scaling problems. Beam strength scales as the square, but mass as the cube. At some point my initial claim that "rider mass is dominant" will stop being true. It might be easier to fabricate the frame as a one-piece casting using I-beams rather than tubes, so that it can be cast and quenched quickly. There doesn't seem to be a lot of research in this area, probably as there's no practical use for "the strongest pure gold beam" but the experiments are expensive (and toxic).

The reason that gold plating and alloys are used is that even small sculptures have structural issues when made of 24 carat gold. The largest pure gold statue I can find online is only 10cm tall and that's labelled as fragile (but that search is fraught as there is so much "huge ... 24 carat gold... plated").

Edit NHinkle suggested in chat that if you float the bike in mercury the structural issues are greatly reduced, so a (solid) gold frame would be ridable, at least for someone willing to immerse themselves in mercury and for the brief time before the gold dissolved in the mercury. The general principle holds though, so "yes, you can make a ridable bike frame out of pure gold". The question is, what would you have to immerse the bike and rider in to balance the weak structure with the load? Water might work, but you'd probably need a denser fluid. Nearly saturated metal salts in water, for example, might work. Or simply doing the build and ride somewhere that gravity is not as strong. The moon, for example, or Ceres.

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If the tubes are solid the mass does not increase with the cube. The volume of cylinder is length X pie X (radius)^2. – Frisbee Jul 16 '14 at 13:04
pie or pi? If pie can I select my own flavor? – David Feb 2 at 8:27
+1 for "the strongest pure gold beam" – Vorac Feb 2 at 11:27
I don't know how you define "statue" but there is a 99.999% pure gold coin measuring 50 cm in diameter and weighing in at 100kg. – Kibbee Feb 2 at 21:03
@Kibbee it's only useful if it can be rolled on its edge. if it has to sit flat then it's no different structurally from a pile of gold dust. By "statue" I meant something that clearly has enough structural strength to hold itself up, and is a shape that needs holding up. – Mσᶎ Feb 2 at 21:32

According to Wikipedia, Gold has an "ultimate tensile strength" of 100 MPa, while steel runs from 400 to 5000. (Carbon fiber laminate is 1600.)

Gold has a specific gravity of about 19, while steel has a specific gravity of about 7.8. So it would take about 4 times as much pure gold by volume, or about 9.7 times as much gold by weight. A 15 pound steel frame would weigh about 145 pounds in gold.

Gold is currently trading about $1300 per (Troy) ounce, so that works out to 145 * 12 * $1300, or $2.26 million. I think even carbon would be cheaper (and lighter).

(And, of course, due to the weight of the frame, the frame strength would have to be beefed up, so you'd need more gold still.)

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The financials explain my short answer of "no", because even if I could afford it I would not be able to bring myself to spend that much making a bike weighing over 7kg :) ...... – mattnz Jul 15 '14 at 20:32
You'd run into tons of problems because the material is so soft. Just think about attaching a wheel to a solid gold fork. Even the pressure from tightening the axle bolts or quick release would deform "drop-outs". Even if they were oversized with extra long bolts to compensate for the added thickness, the bolts would still work themselves loose in no time. – Kibbee Jul 15 '14 at 20:42
@Kibbee Not if you use solid gold axle, washers, and bolts. Really if you are going to spend $2.26 million on a bike are you going cheap the wheels?. – Frisbee Jul 15 '14 at 21:25
You'd have to oversize everything because of the low strength, and use plain bearings because making ball bearings out of gold wouldn't work at all. It's actually a challenging question because "make it bigger" doesn't work - doubling a linear dimension squares the strength but cubes the weight. So no, I think this answer is wrong. – Mσᶎ Jul 15 '14 at 23:18
@Mσᶎ - Yeah, clearly the whole thing gets ridiculous pretty quickly. The frame proper is probably the least problematic aspect. – Daniel R Hicks Jul 17 '14 at 17:19

But to compare 24 carat gold is just not fair.

Bicycles are made of hardened alloys:

  • Aluminium alloy 6061-T6 that is commonly used in bicycles is 6 times as strong as pure annealed aluminium.

  • Steel 1090 alloy is 80 times a strong as iron.

Hardened alloys go back to medieval times.

Hardened 18 carat gold is about the same strength of Steel 1090.
So yes it would be very possible to build a bicycle out of 18 carat gold.
An 18 carat gold frame would be about 2.5 time the weight of Steel 1090.

Gold is a strong metal. They use gold alloys for fillings. Gold does not rust. As a frame material titanium has an edge over gold.

It would be more practical to build a bike out of pure (24 carat) annealed gold than pure annealed iron or pure annealed aluminum.

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Good point that all metallic bike frames are alloys and I guess even carbon has resin involved, not that you'd call that an alloy. – James Bradbury Jul 17 '14 at 12:07

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