You're on the right track with focusing on cable resistance and voltage drop, but let's refine the approach to be more accurate and ensure safety

Here's a breakdown of your thinking and things to consider:
Series Connection

Yes, the switches are in series, meaning the circuit is a single loop. Breaking the circuit at any of the switches will trigger the ESTOP.

Relay Output

The Allen-Bradley 440R relay output is providing the power to the circuit and monitoring its integrity. This is good, as it's designed for safety applications.

Current Draw

While the current draw is likely low, saying "little or no amp draw" is not precise enough for safety calculations. The relay needs some current to determine if the circuit is closed. You need to know what that current is. The 440R datasheet should provide the minimum current required for the relay to register the closed circuit. This is often called the "seal-in current" or "minimum switching current." Look for the value in the datasheet and use that.

Cable Resistance

You're correct in identifying cable resistance as a significant factor due to the long run. 1400 feet total length of the wiring is going to introduce a voltage drop across that distance.

Voltage Drop Calculation

You're on the right track, but let's clarify the formula and ensure we're using the correct figures.

Here's a more detailed approach


Determine the Minimum Current (I)

This is the most crucial piece of information. Get the specification for the minimum current needed by the 440R relay to consider the circuit closed.

Without this, you can't accurately calculate voltage drop and verify circuit integrity.2. Calculate Total Cable Resistance (R)

Find the resistance per foot of 16 AWG wire. You can find this information in standard wire tables online. Copper wire resistance at 20°C is approximately 4.016 ohms per 1000 feet (0.004016 ohms per foot). Multiply the resistance per foot by the total loop length of your wiring: 1400 feet 2 = 2800 feet (1400 feet for the supply and 1400 feet for the return). This is because the current has to travel to the last switch and back. Total Resistance: 2800 ft 0.004016 ohms/ft = 11.2448 ohms3.

Calculate Voltage Drop (Vd)

Use Ohm's Law: Vd = I R (where I is the minimum current you identified from the relay datasheet, and R is the total cable resistance). Example (using a hypothetical 20mA / 0.02A minimum current): Vd = 0.02A 11.2448 ohms = 0.225 Volts.
4.

Verify Sufficient Voltage at the Relay

Determine the voltage supplied by the 440R relay output. Subtract the calculated voltage drop (Vd) from the supply voltage. The remaining voltage must be sufficient for the 440R relay to reliably detect the closed circuit. Consult the 440R datasheet for the minimum voltage requirement.5.

Environmental conditions. Note the resistance values above are at 20 deg C - if temperatures will exceed this in your enclosure be sure to recalculate resistance.

Important Considerations



Safety First

This is an ESTOP circuit. Do not make assumptions. Verify all specifications with the Allen-Bradley 440R documentation. If you are unsure, consult a qualified electrical engineer.

Wire Type

You mentioned #16 AWG. Make sure this wire is suitable for the voltage and environment it's operating in. Consider insulation type, temperature rating, and whether it's solid or stranded.

Connections

Ensure all connections (switch terminals, relay terminals, splices) are properly made and secure. Loose connections can add resistance and create problems. Use appropriate termination methods (e.g., crimped terminals).

Environmental Factors

Consider temperature variations. Resistance of copper wire increases with temperature. If your installation experiences significant temperature swings, you'll need to factor that into your calculations.

Future Expansion

If there is any possibility of adding more switches or extending the wiring in the future, factor that into your calculations now to ensure the circuit remains reliable.*

Testing and Documentation

Thoroughly test the circuit after installation and document all calculations, wire types, and connection details.

In summary


Get the minimum current specification from the Allen-Bradley 440R datasheet. This is the most critical piece of information.2. Calculate the total loop resistance of the wiring.
3. Calculate the voltage drop using Ohm's Law.4. Verify that the voltage remaining at the relay is sufficient for it to reliably detect the closed circuit.
5. Consider all the other factors (wire type, connections, environment, future expansion) and ensure that the circuit is safe and reliable.6. Document your work.Always err on the side of caution when dealing with safety circuits. Good luck! Flag for review