Audit the Payload-Share and Frame-Fit Arithmetic

Ada re-derives payload share, the batching gain, and the frame-fit ceiling from the chapter’s own bytes

ADA · CALCULATION AUDIT

Audit the Payload-Share and Frame-Fit Arithmetic

A single 12-byte reading sent over UDP and IPv4 carries 28 bytes of header (8 for UDP, 20 for IPv4), so only 30% of the packet is useful payload. Batch ten readings and that share jumps to about 81% as the fixed header is paid once, but the batched packet now runs 148 bytes — past the 127-byte ceiling of an IEEE 802.15.4 frame. This audit re-derives the payload share, the batching gain, and that frame-fit limit to ask how far batching can go before the physical link says no.

Companion to the chapter Packet Protocol Overhead — every number here comes from that chapter.

The byte budget is just conservation of bytes: count what carries data, count what carries the protocol, and check whether the resulting packet still fits the physical link.

1. One reading

The chapter's worked example uses a 12-byte sensor reading with UDP and IPv4 headers. The header total is fixed for this packet shape:

H = 8 bytes (UDP) + 20 bytes (IPv4) = 28 bytes

efficiency = P / (P + H) = 12 / (12 + 28) = 12 / 40 = 0.30 = 30%

That leaves 28 / 40 = 70% of the transmitted bytes as protocol packaging before any link-layer framing is counted.

2. Ten readings as a batch

Batching ten readings changes the payload, not the UDP/IPv4 header in this simplified review:

P_batch = 10 × 12 = 120 bytes

efficiency_batch = 120 / (120 + 28) = 120 / 148 = 0.811... ≈ 81%

Case	Calculation	Result
Ten separate packets	10 × (12 + 28)	400 bytes total; 120 payload; 30% useful
One ten-reading batch	120 + 28	148 bytes total; 120 payload; about 81% useful
Bytes not sent	400 − 148	252 bytes saved before link framing

3. The physical frame still gets a vote

A classic IEEE 802.15.4 frame is at most 127 bytes in total. If this same UDP/IPv4 batch had to fit one such constrained-radio frame, it would fail even before link addressing or security bytes were added:

maximum possible upper-layer bytes ≤ 127 bytes, but 120 + 28 = 148 bytes > 127 bytes

What the mathematics buys you: batching improves useful-byte share, but the frame ceiling can turn an efficient-looking packet into a fragmentation risk. The review decision is therefore not "always batch"; it is "batch until freshness, loss exposure, and frame fit still pass."

Every number above is taken from this chapter's own worked example and re-derived step by step.