LoRa Airtime, Duty Cycle & Battery Cost: Spreading Factor Planner

Airtime follows Semtech AN1200.13, LoRa Modem Designer’s Guide, Rev 1 (July 2013), section 4, with the explicit CRC flag shown in FAST-LoRa, equations (1)–(5), attached pages 4–5. The Semtech LoRa Calculator is a companion cross-check tool.

For bandwidth $B$ in hertz, $T_s=2^{SF}/B$. Set $DE=1$ when $T_s>16\,\mathrm{ms}$, otherwise zero (automatic in this planner; see Mobilefish tutorial 17, page 10). Programmed preamble $n_p$ contributes $(n_p+4.25)T_s$. With radio-payload length $L$, implicit-header flag $IH$, CRC flag $C$ and coding-rate index $CR=1\ldots4$:

Total airtime is $(n_p+4.25+n_{pay})T_s$. PHY header and CRC are handled here, so do not add them to the byte input.

Uncoded modulation rate is $SF\,B/2^{SF}$. Multiplying by $4/(4+CR)$ gives a nominal coded information rate, before packet overhead and LDRO effects; it is not application throughput. The calculation sheet also divides entered data bits by packet airtime: radio-payload throughput (including protocol framing) in raw mode, application throughput in LoRaWAN/custom modes. The result text identifies which scope is active.

For entered duty fraction $D$, the one-hour airtime budget is $3600D$ seconds, whole packets per hour are $\lfloor3600D/T_{air}\rfloor$, and the minimum mean start interval is $T_{air}/D$. The off-time equivalent is that interval minus airtime. These are budget identities, not a regulatory scheduler; average hourly use can differ from a particular window containing packet starts.

Battery-side charge is $Q_{TX}=I_{TX}T_{air}$ with explicit conversion to hours, and transmit energy is $VQ_{TX}$ with charge converted to coulombs. Per-message charge adds the entered extra charge and idle current during the rest of the start-to-start interval. Usable capacity divided by mean current gives ideal life. Cost per attempted message is battery price times per-message charge divided by usable capacity. The cost chart uses 1000 messages for readable values.

Illustrative sensitivity starts from the TTN Spreading Factors values at 125 kHz. A $10\log_{10}(B/125\,\mathrm{kHz})$ correction assumes unchanged receiver noise figure and demodulation threshold (Semtech AN1200.13, section 2.2). Link gain relative to SF7 is converted to a distance ratio $10^{\Delta S/(10n)}$ using the log-distance relation in FAST-LoRa equation (7), attached page 5. This is a comparison model, not a radio specification.

The optional pure ALOHA overlap model is derived here: other-node Poisson arrival rate is $(N-1)/T_{msg}$ and the vulnerable interval is $2T_{air}$. Therefore $P_{overlap}=1-\exp[-2(N-1)T_{air}/T_{msg}]$. FAST-LoRa pages 5–6 motivate overlap modeling but include preamble tolerance and SIR/capture effects that this simplified estimate omits.

• One transmission attempt per message; fixed packet settings, bandwidth and battery-side transmit current across the SF comparison. All charge and rated capacity refer to the same battery side and voltage. The 40 mA, 3.3 V, 2400 mAh and price defaults are illustrative scenarios, not component specifications or market prices.
• LoRaWAN mode represents a nonempty uplink data frame with 13 protocol bytes: 1 MHDR + 7 minimum FHDR + 1 FPort + 4 MIC. It uses no FOpts, CR 4/5, explicit header, 8-symbol preamble and payload CRC. Use custom overhead for additional commands or mesh framing.
• The 16 ms LDRO threshold is fixed by the stated model. Check the radio’s actual LDRO setting and supported bandwidths; do not compare a packet configured differently in firmware.
• Battery extra charge is additional to the idle baseline and excludes the TX pulse already modeled. Add wake-up, receive, sensor and regulator effects using battery-side measurements. Cost is allocated per attempted message, including idle consumption at the requested interval; it is not cost per successfully delivered message.
• TTN sensitivity values are typical educational values, not a guaranteed hardware curve. The BW correction assumes thermal-noise scaling; coding-rate effects, hardware offsets, temperature and implementation loss are not modeled. Relative distance assumes the same transmit power, antennas, propagation law and fade margin.
• ALOHA uses equal packet airtimes, equal mean message intervals, independent Poisson starts, one frequency channel and one spreading factor. N includes the tagged node, so N=1 gives zero other-node overlap. All overlaps are treated as destructive; there is no capture or retransmission feedback.

Planning scope, sources reviewed 2026-10-27. Conventional LoRa SF7–SF12, coding-rate indices 1–4, 6–65535 programmed preamble symbols and up to 255 radio-payload bytes. Numeric bandwidth accepts 7.8–500 kHz for comparison; use a value actually supported by your hardware. SF5/SF6, FSK, LR-FHSS and device-specific packet variants are outside scope.

The selected region is context, not an automatic rule set. The entered duty percentage applies to one device sharing a single duty-budget resource, often a sub-band. The one-hour budget does not establish compliance. Check local rules, the standard in force and operator policy for the exact frequency, channel plan, allowed SF/BW, EIRP, dwell time, payload size, averaging period and any listen-before-talk or hopping requirements. A budget is still only a scenario when a region uses a different access rule. No legal limit or price is asserted by the defaults.

The hourly timeline starts a packet at time zero and samples at most 60 starts; tick widths are visual markers. The bar gives long-run mean use, including fractional messages per hour. Battery comparisons are blank where a packet exceeds the requested interval. A duty-budget warning does not automatically reduce your message rate or change the battery calculation.

Life is a constant-capacity, constant-current charge estimate, not a service-life guarantee. Battery pulse capability, voltage sag, cutoff, temperature, self-discharge, aging, joins, ACKs, retransmissions, relay traffic and other channel users need separate treatment. Short-packet ramp energy belongs in extra charge; ramp time is not added to on-air duration. Fixed-duty and Poisson collision views are separate idealisations. The ALOHA number is an overlap probability, not total packet-loss probability or a guarantee for Meshtastic or LoRaWAN.

Published checks distinguish 10 radio bytes (41 ms and 991 ms rounded in Mobilefish tutorial 17) from TTN’s current 10 application byte LoRaWAN example. No absolute range or installation design is provided.