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A fuel-level sender follows a height-related mechanical position, while the driver or controller may need an indication of usable volume. Those quantities are related by tank geometry and installation. A resistance curve intended to represent volume should therefore be built through a sequence: volume target to liquid height, height to sender travel and travel to the electrical value required by the receiver. Keeping those conversions separate makes the calibration reviewable and easier to revise.
Key design decisions
- Define usable empty and full conditions before normalizing volume targets.
- Use the installed tank's volume-height relationship, including internal features and orientation.
- Map the resulting heights through the actual sender mechanism and receiver function rather than assuming equal resistance steps represent equal volume.
Define the volume that the indication represents
Physical tank capacity, usable operating volume and the volume represented by an empty or full indication can differ. Define the relevant operating reference points with the equipment designer. Include reserve, inaccessible liquid and expansion or fill limitations where they are part of the approved tank specification.
Normalize calibration targets within that defined range. If the usable range begins above the physical bottom, a zero-percent usable-volume point is not the same as a completely dry tank. Preserve the underlying absolute volume and height values alongside percentages. This prevents a later change in reserve policy from being confused with a resistor-card manufacturing change.
Build the installed tank's volume-height relationship
For a tank with horizontal cross-sectional area A(h), volume below height h is the integral of area with height, measured from the selected lower reference. A constant-area rectangular tank produces a linear relationship. Tapered, stepped or curved tanks do not, and internal features can change the usable relationship.
Use controlled CAD geometry or a suitable calibrated volume-height dataset for the actual tank orientation. In a nonrectangular tank, liquid height and stored volume are different functions. The same distinction applies when defining a custom resistor curve: the sender's mechanical height response does not automatically represent stored volume.
Calculate target heights before assigning electrical points
Consider a hypothetical tank with an effective horizontal area of 0.02 square meter over its first 0.10 meter of height and 0.04 square meter over the next 0.10 meter. The lower region contains two liters and the upper region four liters, for a six-liter total. Half of that total is three liters.
The three-liter point lies one liter above the lower region. At 0.04 square meter, that additional volume requires 0.025 meter of height, giving a total height of 0.125 meter. Half the total height, 0.10 meter, would indicate only two liters. This example shows why equal height spacing can produce unequal volume spacing even in a simple stepped geometry.
V(h) = ∫ A(z) dz; htarget = V⁻¹(Vtarget)
- A(z) is effective horizontal liquid area at height z.
- Vtarget is the required absolute volume within the defined usable reference.
- V inverse denotes finding the height whose accumulated volume equals the target.
The liquid is static, orientation is fixed and the area model accounts for the relevant tank interior and excluded regions.
Convert each target height to sender travel
Use the actual float linkage, pivot and immersion relationship to obtain the angle or displacement at each target height. A rotary arm generally introduces another nonlinear conversion. Include its mechanical stops and confirm that every target falls within the usable travel.
Keep a table with volume, height and travel as separate columns. If a target height cannot be reached by the mechanism, do not force an electrical value onto an unavailable position. Review the sender geometry or the indicated range. The card's function can shape the output only over the motion the mechanism actually provides.
Determine the resistance required by the gauge or controller
The receiver may convert resistance into a display through its own nonlinear function, excitation current or voltage-divider circuit. Obtain that relationship before assigning resistance points. A linear volume display does not necessarily require resistance proportional to volume.
If the receiver expects a defined resistance at empty, quarter, half and full, map those values to the mechanically calculated travel points. If it uses a digital lookup table, decide whether volume correction belongs in that table or in the card curve and keep one controlled owner for the conversion. Applying both corrections unintentionally can produce a second nonlinearity instead of the intended result.
| Conversion stage | Required input | Check before proceeding |
|---|---|---|
| Usable fraction to absolute volume | Approved empty/full and reserve definitions | Percentages use the same volume reference |
| Absolute volume to liquid height | Installed tank geometry or calibrated dataset | Orientation and internal features are represented |
| Liquid height to mechanical travel | Float, pivot, linkage and immersion model | Targets lie within monotonic usable travel |
| Indicated fraction to required resistance | Receiver transfer function or specified resistance points | Excitation and loading match the intended circuit |
| Travel to manufactured card curve | Combined travel and resistance table | Interpolation and local tolerance are defined |
| Finished system verification | Tank, sender and receiver in the agreed configuration | Independent intermediate volumes are checked |
Add calibration points where the combined map changes rapidly
The combined curve can bend because of tank shape, float geometry or receiver response. Choose point spacing using the allowed volume error, not just an evenly spaced angle grid. Regions near a tank step or a rapidly changing linkage sensitivity may need closer checks.
Retain intermediate validation points that were not used to define the curve. Compare indicated volume with the independent target and identify whether a discrepancy originates in height mapping, mechanism travel or electrical response. A perfect fit at a few listed points can still leave unacceptable error between them, particularly when one conversion is strongly nonlinear.
Keep static calibration distinct from tilt and slosh
The volume-height relationship depends on orientation. Tilt changes the local liquid height at the sender for the same total volume, while motion can create a changing surface. A static level calibration at one orientation cannot establish the displayed behavior under every vehicle or machine condition.
Define the intended reference orientation and any additional conditions requiring system evaluation. Filtering can stabilize a display but introduces delay and does not correct every geometric error. Keep static calibration data separate from dynamic response measurements so the resistance points are not adjusted to compensate one transient test sequence at the expense of the underlying volume relationship.
Deliver the complete conversion chain with the card specification
Provide the tank volume-height data, sender travel map and receiver resistance relationship with matching revision identifiers. State interpolation, units, valid range and local acceptance limits. Include which inputs are measured and which are design targets awaiting verification.
For quotation, send the combined point table and the mechanical envelope, while retaining the source tables that produced it. This allows a tank or receiver revision to be traced to the required card change. The useful deliverable is a resistance function tied to an identified system configuration, rather than a generic empty-to-full resistance range assumed to fit any tank.
Send the volume-to-resistance conversion chain
Provide the tank, mechanism and receiver relationships so the card points represent the intended usable volume.
- Usable empty/full volumes, reserve definition and reference orientation.
- Tank CAD or calibrated volume-height table with internal features represented.
- Float and linkage geometry with measured height-to-travel points.
- Receiver transfer function, excitation, loading and required indication points.
- Combined volume-height-travel-resistance table with interpolation and error limits.
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