140 · Nysa and road statics
One wagon, one mass of goods, two documents asking different questions. Move the load along the beam: the ticket on the left will not change, while the report on the right is recalculated at once.
Without JavaScript you see the starting setting (10 t load 70% of the way from A to B, tare 6 t) and a table of other positions in the section “One beam, two formulas”. The sliders and buttons need JavaScript.
Starting setting: the 10 t load lies 70% of the way from A to B. Move it or change the mass and both calculations will be redone.
Teaching model · not a surviving ticket
Question: what quantity of goods?
10.0t net
mass of goods to be settled
The position of the load does not enter the calculation: net = gross − tare. The form is a modern model, not a copy of an old ticket from Nysa.
Static model · not a WIM measurement
Question: where does the load fall?
10.0t per support
greatest load: support B
The load in kN is the equivalent mass times 9.81. No legal thresholds: the model does not assess compliance with regulations.
The model assumes a beam simply supported at A and B. The tare acts at the middle of the span, the load at point p (from 0.10 to 0.90 of the distance from A to B). The figures in the boxes are calculated live from the settings above; without JavaScript you see the starting setting.
The scale weighed the whole wagon. The tare is subtracted from the gross mass, and the rest is goods, regardless of which side of the wagon they lie on.
net = gross − tare = 16.0 − 6.0 = 10.0 t
Each support carries half the tare and a share of the load that depends on distance. A load nearer B burdens B and relieves A by the same amount.
RA = T/2 + M·(1 − p) = 3.0 + 10.0 × 0.30 = 6.0 t
RB = T/2 + M·p = 3.0 + 10.0 × 0.70 = 10.0 t
RA + RB = 6.0 + 10.0 = 16.0 t = gross 16.0 t
| Position | Net | Support A | Support B | A + B |
|---|---|---|---|---|
| 10% (near A) | 10.0 t | 12.0 t | 4.0 t | 16.0 t |
| 50% (middle) | 10.0 t | 8.0 t | 8.0 t | 16.0 t |
| 90% (near B) | 10.0 t | 4.0 t | 12.0 t | 16.0 t |
| no load (0 t) | 0.0 t | 3.0 t | 3.0 t | 6.0 t |
The last row has no position, because without a load there is no centre of gravity. The ticket then shows 0 t, while the supports still carry the tare.
How to read the diagram. The red marker is the load's centre of gravity, measured from A (0%) to B (100%); the model allows 10–90%. The grey dot on the beam is the centre of mass of the empty wagon, assumed to be at the middle of the span. The bars rise from the road on a single fixed 0–20 t scale, so a change in mass or tare always changes their height.
Units. The tonne is a unit of mass, while the force of a load is mass times acceleration. At g = 9.81 m/s², a mass of 1 t corresponds to approx. 9.81 kN. The report gives the load on a support in equivalent tonnes (kN ÷ 9.81) and in kN; the kN values are rounded to 0.1, so their sum may differ by 0.1 kN.
The building housed the town weigh office and kept the standards of measure. According to the materials given in V2, Nysa probably had the privilege of maintaining a weigh house as early as the beginning of the 14th century, and the scale and the standard ell stood under the arcades [2].
Its present appearance is the result of reconstruction and renovation, so the history of the institution must be distinguished from the appearance of the surviving monument. We do not have the content of the old tickets or the procedure for weighing wagons, which is why the document on the left is our own model. to be checked The dates and description come from V2 and were not reopened here.
The photograph of a façade detail (Jacek Halicki, Wikimedia Commons, CC BY-SA 3.0 PL according to the V2 description) is not embedded, so that the page works offline. Open it on Commons [5]; it shows a detail, not the whole building.
Weighing in motion (WIM, weigh-in-motion) uses sensors that record force as an axle passes. From the signals the system estimates axle loads, and from them the total mass [3]. That is more information than the single figure from a scale.
Our model shows only the principle of distribution over two supports. Measurement in motion must take into account suspension vibrations and station calibration.
In its report on a conference in June 2024, GITD (the Chief Inspectorate of Road Transport) described a discussion of the technical, metrological and legal conditions for automatic weighing [4]. This documents the direction of the work; it does not prove that every roadside point imposes penalties without verification. to be checked Summary from V2.
The references were taken over from V2. They were not reopened in V3, so they are not confirmed here; they are clickable links, not dependencies of the page.
