"Medieval Ship Math" Topic

Obviously there isn't much data on medieval ships, so I'm trying to come up with a rough equation to convert tons (which are more commonly available) into length. I found a dozen ships on wikipedia with lengths and/or tons, and I'm trying to extrapolate from that. here's what I have:
Ship Length Tons T/L
Nina 50 55 1.10
Notorio 55 58 1.05
Pinta 56 65 1.16
Victori 64 85 1.33
Sao Gab 84 100 1.19
Santa M 62 150 2.42
Flor de 118 400 3.39
Antelop 92 450 4.89
Peter P 600 #DIV/0!
Jesus v 700 #DIV/0!
Santa C 120 800 6.67
Santa A 900 #DIV/0!
Great H 165 1000 6.06
Great M 240 1000 4.17
Madre d 165 1000 6.06
Peter v 167 1000 5.99
Grace D 218 1400 6.42
I could just graph them, but if any of you math geniuses out there wish to take a shot at it first, feel free. I've built some smaller ones already, so the bigger ones are of interest.
If anyone can point to a source of data for more ships, more data would make the equation (or graph) more accurate.

Obviously there isn't much data on medieval ships, so I'm trying to come up with a rough equation to convert tons (which are more commonly available) into length. I found a dozen ships on wikipedia with lengths and/or tons, and I'm trying to extrapolate from that. here's what I have:
Ship Length Tons T/L
Nina 50 55 1.10
Notorio 55 58 1.05
Pinta 56 65 1.16
Victori 64 85 1.33
Sao Gab 84 100 1.19
Santa M 62 150 2.42
Flor de 118 400 3.39
Antelop 92 450 4.89
Peter P 600 #DIV/0!
Jesus v 700 #DIV/0!
Santa C 120 800 6.67
Santa A 900 #DIV/0!
Great H 165 1000 6.06
Great M 240 1000 4.17
Madre d 165 1000 6.06
Peter v 167 1000 5.99
Grace D 218 1400 6.42
I could just graph them, but if any of you math geniuses out there wish to take a shot at it first, feel free. I've built some smaller ones already, so the bigger ones are of interest.
If anyone can point to a source of data for more ships, more data would make the equation (or graph) more accurate.

There's a lot of useful data in Venetian Ships and Shipbuilders of the Renaissance by F C Lane.

It's quite complicated because the measures are not consistent – different places had different definitions of a foot and a tonne for example.

Sadly no system will work unless you know the method by which the tonnage was calculated. Different nations used different systems (some of them barely mathematical at all) to define the tonnage and, even then, didn't always stick to that method.

You may hit lucky with sources that have made a sensible attempt at using modern methods of estimation to calculate displacement or any one of the other measures that attempt to define carrying capacity (all referred to as 'tonnage' by some sources) but mostly you won't get comparable values.

Most require you to have at least the length, beam and depth of the vessel to start with; just one of those is insufficient as the shapes of ships' hulls varied so much.

Angus Konstam briefly discusses this in "Sovereigns of the Sea"; 16th century, so not really medieval.

About mercantile shipping but some useful information on ships and how the English did tons burden and how that equates to vessels in military service (Appendix 6)
PDF link

You need to take this question to nautical archaeologists and historians. Those are the people who study this kind of detail.

Some places to ask:
Texas A&M University, Florida State University, and East Carolina University in America, Flinders University in Australia, University of Southern Denmark.

I did research into 16th century ship construction, but got out of nautical archaeology 18 years ago, because I couldn't find a job in it where my wife and moved.

Thanks for the sources. I'll plot these on a graph and work up an average. At 1:600 20 feet is about a millimeter, so that will be close enough.