LastsCalculated
By
Tuesday, April 27, 2004
Lasts Calculations
James C. Bender
March 19, 2003
We will look at the question of computing "lasts". That measurement was used by other nations besides the Dutch. For example, the Swedes also measured "gross tonnage" in lasts.
This information is from Teemu Koivumäki.
These are six Swedish ships:
1.Göta Ark 1634 = 168 x 40 x 17 ft. = 400 läst
2.Svärdet 1625 = 136 x 34 x 16 ft. = 300 läst
3. Fides 1644 = 88 x 26-3 x 14 ft. = 150 läst
4. Rafael 1640 = 103 x 20 x 15-6 ft. = 190 läst
5. Apollo 1623 = 117 x 28-9 x 14 ft. = 230 läst
6. Tu Lejon 1644(prize)= 90 x 27 x 11 ft. = 140 läst
The formula for calculating lasts is:
L x B x D / Factor = Lasts
For the ships listed above, we will calculate the factor that is required to give the "lasts" listed.
|
No. |
Name |
Year |
Length |
Beam |
Depth |
Lasts |
Factor |
|
1 |
Göta Ark |
1634 |
168 |
40 |
17 |
400 |
285.6 |
|
2 |
Svärdet |
1625 |
136 |
34 |
16 |
300 |
243.0 |
|
3 |
Fides |
1644 |
88 |
26ft-3in |
14 |
150 |
215.6 |
|
4 |
Rafael |
1640 |
103 |
20 |
15ft-6in |
190 |
168.1 |
|
5 |
Apollo |
1623 |
117 |
28ft-9in |
14 |
230 |
204.75 |
|
6 |
Tu Lejon |
1644 (prize) |
90 |
27 |
11 |
140 |
190.9 |
One explanation for the great differences in the factor are that lasts seem to have been estimated, without measurements being taken. That would account for the fact that "last" figures are often to the nearest hundred. You might well find "factors" as high as 350. The 168.1 figure is about as low as you might see. What we might consider as "reasonable" factors are in the range of 215 to 250.
If we were going to calculate what we might expect to see as the "lasts" measured for this ships, we might see something like this:
|
No. |
Name |
Year |
Length |
Beam |
Depth |
Lasts |
Factor |
|
1 |
Göta Ark |
1634 |
168 |
40 |
17 |
500 |
228.48 |
|
2 |
Svärdet |
1625 |
136 |
34 |
16 |
300 |
243.0 |
|
3 |
Fides |
1644 |
88 |
26ft-3in |
14 |
140 |
231.0 |
|
4 |
Rafael |
1640 |
103 |
20 |
15ft-6in |
130 |
245.6 |
|
5 |
Apollo |
1623 |
117 |
28ft-9in |
14 |
200 |
235.5 |
|
6 |
Tu Lejon |
1644 (prize) |
90 |
27 |
11 |
110 |
243.0 |
This analysis assumes that "lasts" have a more consistent system for calculation than is apparent from those dimensions and last figures we have. The reason that you might expect there to be a consistent method for calculating "lasts" is that the contemporary English systems all will produce a calulated figure for "tons".
The system in use, from the mid-Seventeenth Century until the end of the "Age of Sail" was as follows:
LK * B * B/2 * 1/94 = Tons
Another English scheme used the actual measured depth of hold, rather than a normalized depth:
LK * B * D * 4/3 * 1/100 = Tons
LK = Length of Keel
B = Beam
D = Depth of Hold
L = Length from Stem to Sternpost
The relationship between LK and L is something like LK = L/1.2 or L/1.25. The divisor is the ratio between the length from stem-to-sternpost and the length on the keel. The D is either a real measurement or else a "normalized" depth. A variation is that for the English, B was measured outside the planking, while the Dutch B was the "moulded" beam, or the beam measurement inside the planking.
The relationship between the two systems is pretty straight-forward.
They all use some length x beam x depth x factor for arriving at either tons or lasts.
The basic pattern is
Gross Tonnage = Length x Beam x Depth * Constant
The Dutch and Swedish "gross tonnage" is measured in "lasts". The English "gross tonnage" is in "tons". The approximate relationship between "lasts" and "tons" is about two "tons" per "last".
There are at least three Dutch ships that we know both dimensions and "lasts":
|
No. |
Name |
Year |
Length |
Beam |
Depth |
Lasts |
Factor |
|
1 |
Ter Goes |
1625 |
125 |
29 |
11.5 |
200 |
208 |
|
2 |
De Zon |
1632 |
128 |
31.5 |
12 |
250 |
194 |
|
3 |
Aemelia |
1632 |
144 |
34 |
14.3 |
300 |
233 |
This information is from Ab Hoving's book:
Nicolaes Witsens Scheeps-Bouw-Konst Open Gestelt, published in 1994.
This is how we might compute the "lasts", if we were trying to compute "reasonable" lasts:
|
No. |
Name |
Year |
Length |
Beam |
Depth |
Lasts |
Factor |
|
1 |
Ter Goes |
1625 |
125 |
29 |
11.5 |
180 |
231.6 |
|
2 |
De Zon |
1632 |
128 |
31.5 |
12 |
200 |
241.9 |
|
3 |
Aemelia |
1632 |
144 |
34 |
14.3 |
300 |
233.0 |
The factor for the Aemilia already fits the "reasonableness" criterion.
