Formula for ballast needed?

[paul ron]

for our model use, I'll bet a cheap student gizmo is still overkill.

i just thought it would be interesting to see how its used.

 

[Bob Cleek]

for our model use, I'll bet a cheap student gizmo is still overkill.

i just thought it would be interesting to see how its used.

You are absolutely correct. It's not likely that a modeler would require a professional drafting instrument of any kind. In most instances the student level instruments get the job done if used with care. The one exception I would note, however, would be instruments which are marked with scales. The scaling affects the accuracy. There's a big difference between the scale on a classic machine engraved rule and a cast plastic one!

Actually, there's a trick of the trade for taking accurate readings with a planimeter. It's critical when tracing the edge of the irregular plane with a planimeter that you keep the cursor exactly on the edge line. While this is easier with planimeters that have good magnifying "bullseye" cursors, it is still a tedious exercise, and a shake of the hand can cause an error. To minimize the error, one can take repeated measurements, five or ten being quite adequate, I'd think. Any measurement which is obviously greatly erroneous can be discarded, and then the total area of the measurements retained thereafter is then divided by the number of measurements retained to yield an average measurement which, in theory, at least, increases the accuracy.

I suppose I should also mention that anybody who may be considering acquiring a planimeter should identify the type of scale measurements they want to obtain. There are a lot of different options, the most obvious being metric or imperial measurements and the range of measurement, e.g. feet, yards, meters, etc. Some planimeters can be set for a wide variety of measurements, while others are limited.

Another caveat about planimeters, and any measurements relevant to period ship modeling, is that the definition of measurements, for instance, the foot, was not internationally standardized until 1959! (Yes, 1959. Surprised me, too.) Particularly in 17th and 18th Century Europe, the length of a "foot," varied considerably, with many nations, and, indeed, cities within nations, having their own definition of the length of a foot. As seen from the chart below, for example, in an Amsterdam shipyard, a "foot" was 283.133mm, while in a Rotterdam shipyard, a "foot" was 312.43mm, and a foot was 296.9mm in Sweden, and 305.287mm in Scotland! There were 9 different "foot" measurements for various cities in the Netherlands and 21 different "foots" in Germany and on top of all that confusion, some changed from time to time. See: https://en.wikipedia.org/wiki/Foot_(unit)

Thus, if you are trying to calculate the ballast required for a given ship, you will have to begin by identifying the measurement system used to describe its size and then translate that to present day standards from which you can calculate the ballast needed accurately. If you don't do this, your ballast calculation can be somewhat off the mark. This circumstance is also applicable to all scale measurements. A ship that is 150 feet long could easily be over or under by several feet in length if the actual contemporary measurement standards aren't taken into account.

Vienna	Austria	Wiener Fuß	316.102[46][37]
Tyrol	Austria	Fuß	334.12[39]
Ypres (Ieper)	Belgium	voet	273.8[50]
Bruges/Brugge	Belgium	voet	274.3[50]
Brussels	Belgium	voet	275.75[50]
Hainaut	Belgium	pied	293.39[43]
Liège	Belgium	pied	294.70[43]
Kortrijk	Belgium	voet	297.6[50]
Aalst	Belgium	voet	277.2[50]
Mechelen	Belgium	voet	278.0[50]
Leuven	Belgium	voet	285.5[50]
Tournai	Belgium	pied	297.77[43]
Antwerp	Belgium	voet	286.8[50]
China	China	tradesman's foot	338.3[51]
China	China	mathematician's foot	333.2[51]
China	China	builder's foot	322.8[51]
China	China	surveyor's foot	319.5[51]
Moravia	Czech Republic	stopa	295.95[39]
Prague	Czech Republic	stopa	296.4[45]	(1851) Bohemian foot or shoe
301.7[40]	(1759) Quoted as "11 pouces⁠1+ 3/4​ ⁠ lignes"[Notes 1]
Denmark	Denmark	fod	313.85[46]	Until 1835, thereafter the Prussian foot
330.5[40]	(1759) Quoted as "⁠2+ 1/2​ ⁠ lignes larger than the pied [of Paris]"[Notes 1]
France	France	pied du roi	324.84[52]	[Notes 2]
Angoulême	France	pied d'Angoulême	347.008[53]
Bordeaux (urban)	France	pied de ville de Bordeaux	343.606[53]
Bordeaux (rural)	France	pied de terre de Bordeaux	357.214[53]
Strasbourg	France	pied de Strasbourg	294.95[53]
Württemberg	Germany	Fuß	286.49[39]
Hanover	Germany	Fuß	292.10[39]
Augsburg	Germany	römischer Fuß	296.17[44]
Nuremberg	Germany	Fuß	303.75[44]
Meiningen-Hildburghausen	Germany	Fuß	303.95[39]
Oldenburg	Germany	römischer Fuß	296.41[39]
Weimar	Germany	Fuß	281.98[39]
Lübeck	Germany	Fuß	287.62[46]
Aschaffenburg	Germany	Fuß	287.5[43]
Darmstadt	Germany	Fuß	287.6[43]	Until 1818, thereafter the Hessen "metric foot"
Bremen	Germany	Fuß	289.35[46]
Rhineland	Germany	Fuß	313.7[51]
Berlin	Germany	Fuß	309.6[51]
Hamburg	Germany	Fuß	286.8[51]
Bavaria	Germany	Fuß	291.86[39]
Aachen	Germany	Fuß	282.1[44]
Leipzig	Germany	Fuß	282.67[39]
Dresden	Germany	Fuß	283.11[39]
Saxony	Germany	Fuß	283.19[46]
Prussia	Germany, Poland, Russia etc.	Rheinfuß	313.85[46]
Frankfurt am Main	Germany	Fuß	284.61[39]
Venice & Lombardy	Italy		347.73[39]
Turin	Italy		323.1[51]
Rome	Italy	piede romano	297.896[53]
Riga	Latvia	pēda	274.1[51]
Malta	Malta	pied	283.7[51]
Utrecht	Netherlands	voet	272.8[51]
Amsterdam	Netherlands	voet	283.133[42]	Divided into 11 duimen (inches, lit. 'thumbs')
Honsbossche en Rijpse [nl]	Netherlands	voet	285.0[42]
's-Hertogenbosch	Netherlands	voet	287.0[42]
Gelderland	Netherlands	voet	292.0[42]
Bloois (Zeeland)	Netherlands	voet	301.0[42]
Schouw	Netherlands	voet	311.0[42]
Rotterdam	Netherlands	voet	312.43[43]
Rijnland	Netherlands	voet	314.858[42]
Norway	Norway	fot	313.75[54]	(1824–1835)[Notes 3] Thereafter as for Sweden.
Warsaw	Poland	stopa	297.8[55]	Until 1819
288.0[43]	(From 1819) Polish stopa
Lisbon	Portugal	pé	330.0[44]	(From 1835)[Notes 4]
South Africa	South Africa	Cape foot	314.858[56]	Originally equal to the Rijnland foot; redefined as 1.033 English feet in 1859.
Burgos and Castile	Spain	pie de Burgos/ Castellano	278.6[40]	(1759) Quoted as "122.43 lignes"[Notes 1]
Toledo	Spain	pie	279.0[40]	(1759) Quoted as "10 pouces 3.7 lignes"[Notes 1]
Sweden	Sweden	fot	296.9[46]	= 12 tum (inches). The Swedish fot was also used in Finland (jalka).
Zürich	Switzerland		300.0[51]
Galicia	Ukraine, Poland	stopa galicyjska	296.96[43]	Part of Austria–Hungary before World War I
Scotland	United Kingdom		305.287[57]	[Notes 5]

​

 

[paul ron]

the principal of this gizmo is interesting. it measures the circumference of the shape to determine the area. clever!