Did plot triumph over physics in the climax of the film “*Titanic*?” Could Jack have shared the raft of flotsam with Rose, or would both actors have sunk beneath the waves?

Let’s examine the math calculations for floating this improvised raft, made from a door that broke away from the *Titanic*.

## Setting the Stage and the Goal

The primary question is whether they sink or float under ideal conditions, but we’ll also explore exactly how big the raft would need to be, in order to support 2 people.

We set the target of “floating” to mean that the total volume of the wood could be just at the water line, but that the people remain dry on top.

The requirement will be that the weight of the sea water that would be displaced by the entire raft must equal or exceed the weight of the raft, plus any survivors.

## Weight, Mass, Density, and Buoyancy via the Archimedes Principle

Normally, it is easy to measure the weight of an object, whether using a spring-loaded weigh scale or a balance.

The density of an object is equal to its weight divided by its volume. Again, it is easy to calculate the volume of a regular solid such as a cube, which equals the length times width times height.

The Greek philosopher Archimedes realized that the volume of water displaced by any fully-submerged object is the same as the volume of the object. Therefore, an irregularly-shaped crown displaces the same volume of water as a cube of the metal from which it was cast.

The weight of the displaced water equals the volume of water times its density.

In general, the buoyancy provided by any fluid equals the mass that was displaced, multiplied by the acceleration due to gravity. This translates mass into “dynes.” However, the downward force opposed by the buoyancy is *also* the mass of the object *multiplied by gravity*.

This article will, therefore, omit multiplying weights by “9.8M/s^2,” since the acceleration due to gravity will be irrelevant to the question of sinking or floating.

This leaves a slight error due to the buoyancy of the object in air. This is about 0.08 pounds/foot^3 or (0.08lb/2.2lb/Kg) per (1foot/3.28M)^3 = .0363636… Kg/0.02834M^3 = 1.283Kg/M^3. Compared to water’s density of 1000Kg/M^3, this error just over 0.1%. That is extremely minor, compared to the assumptions about the type of wood or size of the door we’ll be making.

The *Archimedes Principle* is that a submerged object’s effective weight is reduced by the weight of the displaced fluid. If an object is less dense than the fluid it displaces, it will float, partially submerged. The volume that is submerged will displace enough fluid to match the weight of the whole object.

**Click to Read Page Two: Assumptions and Physical Constraints for the Titanic Flotsam Raft**

Mike DeHaan says

For Will, Stooge & Moioci, who pointed out that the door was probably much thicker…

“Arghh, you’re all extremely likely to be correct”.

Assume 1.5″ rather than 0.5″? So we only need 1/3 the number of doors that I had calculated?

Thank you for taking the time to let us know.

moioci says

Wait a minute. The NYT site describing the 1/2-inch thick piece of door says, “This relic was once a **thicker block** that years ago was cut up into tiny pieces, which sold for four figures each.” Think about it. Even in today’s world of very cheap construction, a half inch would be very flimsy, even for a closet door, let alone a stateroom door. I vote the actual door was at least an inch thick, possibly more.

Stooge says

Your assumption about the thickness of the original door is wrong: as the blurb for the Titanic door fragment clearly states, the piece being sold is 0.5 inches thick, but it “was once a thicker block that years ago was cut up into tiny pieces”.

Will says

Really? You’re going with a half-inch thick door as “realistic”? How about this: you show me just one wooden door that’s a half-inch thick and I’ll allow that assumption. Meanwhile, here’s a standard 30×80 door:

http://www.homedepot.com/Doors-Windows-Interior-Doors/h_d1/N-5yc1vZbuhv/R-202523949/h_d2/ProductDisplay?catalogId=10053&langId=-1&storeId=10051

1.375 inches, or about 3.5 cm, about as thick as your “burglar” door.

Edward says

Bothhh Cannot Sorvive On dahhh Sea With Such Wavesss And High tides ,,,,,, ???

W says

For the door to support their weight it would have to weigh approx. 560 lb. to float level with the sea surface and more to keep them above. Take some strength to launch it!

Nara says

I guess neither Jack, nor Rose (and she was smart, too) were aware of Archimedes principle…too bad, maybe Jack could have lived a day longer or so…but then, the ending had to be gut wrenching, after all.