The Second Resistance: What Waves Add and Why It Rules So Much

Calm-water resistance, the floor this academy's resistance course walks through, is a solved, measurable, well-behaved quantity. The moment real weather arrives, a second resistance appears on top of it: added resistance in waves, the extra force the seaway extracts from the ship at the same speed and loading. It is the hardest routinely-needed number in ship performance, and this course is about earning the right to use it.

Definition and scale

Added resistance is a difference: resistance in waves minus resistance in calm water, everything else held equal. It is a pure wave effect: wind on the superstructure is a separate, additional term with its own physics and its own correction methods.

Two facts set its scale. First, it is large: for a typical merchant ship, moderate head seas (nothing a master would call heavy weather) can add tens of per cent to the power required to hold speed, the same order of magnitude as severe hull fouling. A voyage's weather exposure is often among the largest single deviations between predicted and actual consumption.

Second, it grows quadratically with wave amplitude. Double the wave height and added resistance roughly quadruples. This single scaling law explains most of the subject's operational character: the difference between a 2-metre and a 3-metre sea is not "a metre": it is more than double the added resistance. It also explains why routing around weather (the choice of which waves to meet) is worth real money, and why every formula in this course is written in terms of amplitude squared.

Direction matters almost as much. Head seas are the expensive direction; beam seas cost less; and following seas can, in the right speed and wavelength combinations, cost nearly nothing: the wave field can even push the ship slightly. Any method that only knows head seas (and for decades, most didn't) misses the majority of a real voyage's headings.

The two terms in a real service record

This lesson has set wind aside as a separate term and left it there. Which of the two is the bigger correction is a question a service record can answer. Two sister VLCCs of about 317,000 DWT, each logging one record a minute, carry a performance pipeline that estimates the wind correction and the wave correction separately, minute by minute while they are under way, each as a share of the shaft power that same minute recorded. Take the cleaned records, the minutes where the pipeline's own quality flag passed, speed, power and revolutions all read a real number, and speed and power are both above zero, 191,244 of them on VLCC1 and 380,443 on VLCC2 (the same pipeline's filter chain, as our ISO 19030 course reports it, passes 191,248 and 380,459 usable records; the extra conditions here keep four and sixteen fewer): the wave term is the larger of the two through the body of the distribution. Its median share of that power is 1.1 per cent on VLCC1 and 2.6 per cent on VLCC2, where wind's medians over the same records are 0.1 and 0.6 per cent. At the ninetieth percentile the wave correction is 7.1 and 10.2 per cent, against wind's 6.0 and 6.9.

Two features of that record matter more than the ranking. The first is its shape. Half of those steaming minutes sit below the medians just quoted, and the expensive weather lives in a thin tail: one minute in ten is above the ninetieth-percentile figures, and the worst single minutes reach 21.3 per cent of shaft power on VLCC1 and 48.7 per cent on VLCC2. The tens of per cent this lesson opened with are real, but on these two records they are what the tail costs and not what the median hour costs, and these are two very long ships: ship length decides where a given sea lands on the response curve, and the sea that sits on a VLCC's reflection plateau sits on a feeder's resonance peak. That is exactly why routing around weather pays, and why a flat weather allowance in a voyage estimate is the wrong shape of answer.

The second is what the wind term does at its own extreme. In these cleaned records VLCC1's largest wind correction is 43.4 per cent of shaft power and VLCC2's is 34.7 per cent. But a maximum is one minute out of hundreds of thousands, and a share of power can be inflated by a collapsed denominator as easily as by a real force, so neither extreme carries the weight of a median. Notice, too, what these records are: the cleaned minutes defined at the top of this section. Whatever those filters removed is not in these figures, and anything dropped for being heavy weather would make these shares an understatement. That is the problem the monitoring paragraph below comes to.

Four places the number is decisive

Sea trials. Trial runs are corrected back to calm water, and the wave correction is the correction chain's hardest link: our ISO 15016 course gives it a full lesson. The methods used there are the very ones this course pair dissects; the standard's 2025 generation changed them, and Part 2 opens with the story of why.

Performance monitoring. ISO 19030-style analysis takes the opposite approach: rather than correct weather records, it filters them out, affordable because continuous data is abundant. But note what that discipline concedes: the weather periods go unanalysed, though the fuel burned in them is real. Understanding added resistance is how an analyst audits the records the filters discard.

Weather routing. A routing tool compares candidate routes by predicted cost, and the dominant cost difference between routes is added resistance. The quality of the routing decision is capped by the quality of the added-resistance model inside it, and by the vessel data feeding that model.

Claims and clauses. Charter-party performance disputes turn on what the weather "should have" cost. Whoever holds the more defensible added-resistance estimate holds the stronger case.

Why it is genuinely hard

The subject's difficulty is honest, and it is double. The response is complex: added resistance depends on wave height, period and direction, and simultaneously on the ship's length, beam, draught, fullness, mass distribution, speed and trim, through two distinct physical mechanisms (next lesson) that dominate in different conditions. And the input is uncertain: outside a trial with wave measurement, the sea state itself (the height, period and direction fed into any formula) comes from hindcasts, forecasts or observations, each with error bars of their own. Even a perfect method inherits the sins of its wave data.

The subject is taught here in two parts, and this course, Part 1, takes the problem apart in exactly that order: the two mechanisms (next lesson), how one hull answers each wavelength (the response curve every later method is secretly a model of), the sea and its spectra, where wave data actually comes from and the quiet confusion of wave periods, and the methods landscape of tanks, CFD and formulas. Part 2 then builds the working method: the SNNM regression and its rise to regulatory standing, what actually drives its terms, the honest treatment of real irregular seaways as windsea plus swell, what a validation does and does not promise, and finally where the number gets spent (trials, monitoring, routing, claims), with the uncertainty it should always carry.