The Complete Guide to CP and W′: A Hyperbolic Model That Understands Pacing Better Than FTP, from Wuling to Criterium Racing

Many cyclists treat FTP as the single number defining their ability: FTP goes up and you’re stronger; it drops and you’re in bad form. But if you’ve ever been drained by repeated sprints in a criterium, blown up on the short steep climbs of Fengguizui and ruined the rest of the ride, or gone out too fast in the first 400 meters of a road race only to see the whole thing fall apart, you know that “one number” can’t explain what actually happens in a race.

Critical Power (CP) and W′ (W prime) offer two numbers: one describes your level of “how long you can sustain effort without falling apart,” and the other describes “how much reserve you have left to spend above that level.” The running version is Critical Speed (CS) and D′. This two-parameter model isn’t a magic bullet, but it’s currently the cleanest framework for describing the “intensity—time to exhaustion” relationship, and it translates most directly into pacing decisions.

This article will cover the math, physiological meaning, testing methods, controversies, and pacing applications of CP/CS and W′/D′ in real Taiwan scenarios (Wuling long climbs, Fengguizui, Beiyi, riverside flat time trials, criteriums, road running, and trail running), all in one go.

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1. The Hyperbola: What This Model Is Actually Saying

1-1 Starting with a Very Intuitive Observation

You can push 1000 watts for a few seconds, 400 watts for a few minutes, 250 watts for an hour, and 200 watts all day. Plot “intensity” against “time you can sustain it” on graph paper, and you get a curve that drops to the lower right, then gradually flattens out.

The key point: this curve flattens out but never reaches zero. It approaches a horizontal asymptote. The height of that asymptote is CP (Critical Power).

In other words, the mathematical definition of CP is: the value that power converges to as sustainable time approaches infinity. Below CP, theoretically you can ride forever; above CP, you will eventually have to stop, and how far above determines how long you can last.

1-2 The Equation of the Two-Parameter Model

The most common form is:

P = CP + W′ / t

• P: the maximum average power you can sustain for that duration (watts)
• CP: Critical Power (watts)
• W′: the area above the curve, in joules (J), i.e., work
• t: sustainable time (seconds)

Rearranging gives a more useful linear form:

W = CP × t + W′

Here, W is the total work done in that time (joules) = average power × time. The meaning of this equation is: the total work you do in any all-out effort equals the part from “the CP faucet flowing continuously,” plus a fixed allowance W′ “poured out once from the bucket.”

The running version is structurally identical:

D = CS × t + D′

• D: distance covered in that time (meters)
• CS: Critical Speed (meters/second)
• D′: the area above the curve, with units of distance (meters)

1-3 Feeling How Brutal This Curve Is with Hypothetical Numbers

All numbers below are fictional examples created solely to illustrate the math. They are not research findings, nor are they averages for any population. Please do not compare them to your own or anyone else’s abilities.

Suppose a cyclist has CP = 250 W and W′ = 20 kJ (20,000 J). Then:

Target Power (W)	Above CP (W)	Theoretical Sustainable Time	Conversion
275	25	20000 ÷ 25 = 800 seconds	~13 min 20 sec
300	50	20000 ÷ 50 = 400 seconds	~6 min 40 sec
350	100	20000 ÷ 100 = 200 seconds	~3 min 20 sec
450	200	20000 ÷ 200 = 100 seconds	~1 min 40 sec
250	0	Theoretically infinite	(Obviously not in practice)

Notice how brutal this comparison is: going from 250 W to 350 W is only a 40% increase, but sustainable time drops from “theoretically infinite” to 3.5 minutes. This is the essence of the hyperbola: the closer you are to CP, the more extreme the sensitivity of time to power. For this reason, the cost of “pushing 10 more watts” in a race is completely different depending on where you start—10 watts below CP is almost free, but 10 watts above CP could make you blow up two minutes earlier.

1-4 The “Area” Intuition of W′

Look again at W = CP × t + W′. Suppose the same cyclist rides at 300 W for 400 seconds:

• Total work = 300 × 400 = 120,000 J
• The CP portion = 250 × 400 = 100,000 J
• The remaining 20,000 J is the W′ that gets used up

In other words, W′ is “the watts above CP, multiplied by the seconds you hold them, accumulated into a total allowance.” This concept of “excess × time = allowance” is the foundation for all the pacing applications that follow.

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2. The Faucet and the Bucket: A Useful but Careful Analogy

2-1 The Analogy Itself

Imagine you have a bucket with a faucet above it:

• The faucet’s continuous inflow = CP. It’s always on, with a fixed flow rate. This is your supply that comes “without cost.”
• The water in the bucket = W′. This is a one-time reserve. You can pour it out, but once it’s gone, it’s gone.
• Your rate of water use = your current power.

So:

• When power is below CP: the faucet brings in more than you use, and the bucket is recharging.
• When power equals CP: it’s exactly balanced, and the bucket neither gains nor loses (the theoretical tipping point).
• When power is above CP: the faucet isn’t enough, and the difference must be scooped from the bucket—the bucket is draining.
• When the bucket runs dry: you’re forced to drop below CP—that’s “blowing up”—not that you can’t move, but you can no longer hold that intensity.

The greatest value of this analogy is that it clarifies three things that are often confused: (1) exceeding a threshold doesn’t break you instantly; it starts a clock; (2) the cost accumulates; (3) the cost can be “paid back,” as long as you’re willing to drop below CP.

2-2 Where This Analogy Is Imprecise (Very Important)

This is a simplified illustration of the model, not a precise physiological description. At least a few points need to be taken with a grain of salt:

1. The bucket is not a physical “thing.” There is no container in your body holding 20 kJ. W′ is a parameter fitted from the model; it corresponds to a complex set of physiological phenomena (discussed in Chapter 4), not a directly measurable energy store.
2. The faucet’s flow rate is not constant. CP after three hours of riding is not the same as CP when fully rested (durability/CP decline, discussed in Chapter 7). The faucet gets smaller.
3. Recharge is not linear. The simplest model assumes “the more you’re below CP, the faster you recharge at a fixed rate,” but in reality, recharge is closer to exponential, and the closer you are to CP, the slower the recharge. Coasting at CP minus 5 W is nothing like resting at CP minus 100 W in terms of recharge efficiency.
4. The bucket’s capacity changes. W′ changes with training, fatigue, daily form, temperature, and nutritional status. It is not a constant carved into your body.

So: using this analogy for decision-making direction is good; using it for precise calculations to the decimal point is dangerous.

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3. CP, FTP, MLSS, LT2: Similar Concepts, but Don’t Treat Them as the Same Number

This is where most people get confused. These four terms all describe the “aerobic/anaerobic boundary zone,” but their definitions differ, their testing methods differ, and the numbers they produce differ.

Term	Essential Definition	How It’s Obtained	Common Misconception
CP (Critical Power)	The mathematical asymptote of the power–duration hyperbola	Multi-stage all-out tests, 3MT, power curve fitting	Thinking it’s the same as FTP
FTP (Functional Threshold Power)	Practically defined as “the maximum average power sustainable for about one hour”	Often estimated by discounting a 20-minute test result, or by doing a longer test directly	Thinking the 20-minute discounted result is always accurate
MLSS (Maximal Lactate Steady State)	The highest intensity at which blood lactate remains stable without continuously rising	Requires multiple constant-intensity tests on separate days plus blood sampling; laboratory-oriented	Thinking it can be obtained from a single test
LT2 / Second Lactate Threshold	The intensity zone where lactate begins to accumulate noticeably and ventilation shows a second inflection	Incremental exercise test with blood sampling or gas analysis	Thinking it’s a “point,” when it’s actually a band/zone

3-1 Why CP Is Usually Slightly Higher Than the “20-Minute Discounted” FTP

A very practical observation is: CP fitted from short, medium, and long all-out efforts is often slightly higher than FTP estimated by discounting a 20-minute test. There are at least two reasons:

• Mathematically: CP is an asymptote—it’s the limit for “infinite time”—while the common FTP estimation method asks you to approximate “one hour sustainable.” But one hour is not infinite time; the maximum average power for one hour theoretically still contains a small contribution from W′. Conversely, the result of a 20-minute test contains a significant proportion of W′, and the discount factor is only an empirical correction, not tailored to each individual.
• Individual differences: The discount factor is unfair to people with “large W′” versus “small W′.” Someone with a large W′ (a sprinter) can produce a better-looking number in a 20-minute test thanks to W′, and applying the same discount factor will overestimate their CP; someone with a small W′ and endurance-oriented profile may be underestimated. This is the core reason the two-parameter model is more useful than the single-parameter FTP—it separates out “how big your bucket is” for individual treatment.

3-2 How to Practically View These Numbers

• Don’t substitute one for another. If your training plan is written in FTP percentages, use FTP for the plan; if you’re doing W′ balance race pacing, use the fitted CP. Forcing CP into the FTP field will push all training zones higher overall.
• Note which method was used in your records. “My FTP improved by 8 W” is meaningless if one measurement came from a 20-minute discount and the other from a three-stage fit.
• Treat them as different estimates of the same physiological zone. They all describe the upper edge of “aerobic supply can hold, and metabolites can still be cleared.” The differences are usually small, but consistency in direction is more useful than precision in absolute value.

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4. How to Test: Four Routes and Their Sources of Error

4-1 Safety Prerequisites (Please Read This First)

CP/CS testing is essentially near-exhaustion maximal effort, with high intensity and significant cardiovascular load. Before you start:

• If you have cardiovascular disease, poorly controlled hypertension, a history of chest pain or tightness, arrhythmia, recent infection or fever, or have been sedentary for a long time, consult a physician before performing any maximal effort test.
• If during the test you experience chest pain, chest tightness, unusual breathlessness, dizziness, blurred vision, palpitations, nausea, cold sweats, or unilateral limb weakness, stop immediately. Don’t “push for another thirty seconds.”
• This article provides general training and pacing information and cannot replace individual assessment by a physician or sports medicine professional.
• For outdoor testing, be sure to consider traffic and environmental safety. Judgment and peripheral vision decline under maximal effort. Choose roads with minimal traffic, good pavement, and no intersections or pedestrians. Avoid rush hour and wet weather. This article does not encourage racing on open roads; on descents, completely abandon any pursuit of data—safety always comes before any test result. If you can use a trainer or a closed course, don’t go on the road.

4-2 Method 1: Multi-Stage All-Out Testing (on Different Days)

This is the classic and usually most reliable method.

Concept: Choose three durations with sufficiently different lengths and perform one all-out maximum average power effort for each. A common approach is “one short, one medium, one long,” for example picking three points in the range of a few minutes to over ten minutes. Plug each stage’s (time, total work) into the linear regression W = CP × t + W′; the slope is CP, and the intercept is W′.

Demonstration with hypothetical numbers: (fictional example values below)

• 3-minute (180-second) all-out, average 340 W → total work = 340 × 180 = 61,200 J
• 12-minute (720-second) all-out, average 275 W → total work = 275 × 720 = 198,000 J

CP = (198,000 − 61,200) ÷ (720 − 180) = 136,800 ÷ 540 ≈ 253 W
W′ = 61,200 − 253 × 180 ≈ 61,200 − 45,600 = 15,600 J ≈ 15.6 kJ

(In practice, you’d use three or more stages for the regression; two stages are just to make the calculation clear.)

Sources of error for this method:

Source of Error	What Happens	How to Reduce It
Uneven pacing	Going out too hard early and fading too much later means that stage’s “maximum average power” is actually below your true ability	Set a target power beforehand; don’t overdo the first 30 seconds; treat the test like a standalone race, not a casual effort
Residual fatigue	Doing all three stages on the same day or consecutive days means later stages are dragged down by earlier ones	Do them on separate days with enough recovery in between; randomize the order rather than always doing “short first, long last”
Test durations too close together	For example, picking 8, 10, and 12 minutes puts all three points on nearly the same part of the curve, making the regression slope highly unstable	Spread the durations out; the short one should be truly short, and the long one truly long
Inconsistent power meters	Trainer power and road power meter differ by a few percent; mixing them contaminates the regression	Use the same device and the same venue conditions for all tests
Psychological state	Some people hold back when they know “there’s still another test to do”	Treat each stage as if it’s the only one; once it’s done, it’s done
Interference from very short efforts	Including data under 1 minute in the regression is dominated by neuromuscular explosiveness, inflating W′ and deflating CP	Generally avoid including very short all-out efforts in this linear fit

4-3 Method 2: The 3-Minute All-Out Test (3MT) Concept

Concept: Go all-out from start to finish for a full three minutes, with no pacing or holding back. The theory is that the early part burns through W′, and by the final portion, the power you can output is only “the faucet’s flow”—approaching CP. So the common approach is:

• CP estimate = average power over the final portion of the test (e.g., the last 30 seconds)
• W′ estimate = the sum of the work done above that CP value during the entire test

Advantages: Done in one go, no need to split across days, very appealing for people with limited time.

Sources of error and cautions:

• You must truly go all-out from the first second. This goes against everyone’s racing instinct. If you’re thinking “save a little for later,” you won’t burn through W′ early, the final portion’s power will be overestimated, and CP will come out too high.
• Resistance settings affect the result. This test is very sensitive to the trainer’s resistance mode. The same person can get noticeably different numbers under different resistance settings. To compare, you must retest with exactly the same settings.
• Extremely uncomfortable. This is one of the worst subjective experiences of all tests, so retest consistency is easily affected by psychological state.
• Not recommended for beginners as a first way to learn about themselves. It’s safer to build a baseline understanding with a more moderate staged test first.

4-4 Method 3: Fitting from Your Training Data’s Power Curve

Almost all power analysis software now plots a “Mean Maximal Power curve”: it draws a line through your best average power for every time duration in your historical data. Theoretically, as long as the points on the curve are “true,” you can fit CP and W′ directly from it.

Advantages: No extra testing required, allows continuous tracking of changes, and shows how the curve shape differs across periods.

This method has the most errors, so be especially careful:

1. Non-all-out data contaminates the curve. If you’ve never truly gone all-out for a given duration, that point will be too low, pulling the entire curve down and underestimating CP. This is the most common problem—most people have real data for “10 seconds” and “20 minutes,” but have never seriously done “3 minutes” or “8 minutes.”
2. Points from different dates are mixed together. The 5-minute best on the curve might come from a peak-form period three months ago, while the 20-minute best is from last week’s fatigued data. These two points don’t belong to the same curve, so the fitted parameters have no physiological meaning.
3. False high points from descents and drafting. Some short-duration high-power readings come with assistance from gravity or being pulled along in a group; the contexts aren’t equivalent.
4. Improper time window settings. Fitting with “best of the last 90 days” versus “best of the last 42 days” can produce noticeably different CP values. When comparing before and after, be sure to use the same window length.

Practical advice: Treat power curve fitting as a trend-monitoring tool (see how the shape changes, which durations have gotten stronger), not as precise measurement. If you truly need a trustworthy number, go back to a well-designed staged test.

4-5 Method 4: Running CS and D′—Estimating from Personal Bests at Different Distances

Running has the advantage that “distance” is much cleaner than “power,” and most runners already have personal bests (PBs) at various distances.

Method: Take recent best times for two or more distances and plug them into D = CS × t + D′.

Demonstration with hypothetical numbers: (fictional example values below)

• 1500 m PB: 5:00 = 300 seconds
• 5000 m PB: 19:20 = 1160 seconds

CS = (5000 − 1500) ÷ (1160 − 300) = 3500 ÷ 860 ≈ 4.07 m/s
Converted to pace = 1000 ÷ 4.07 ≈ 246 sec/km ≈ ~4:06 per kilometer

D′ = 1500 − 4.07 × 300 ≈ 1500 − 1221 = ~280 meters

The physical meaning of D′ is very visual: it represents “the total extra distance you can run above CS.” If you run faster than CS, every second is spending down that 280-meter reserve in advance.

Sources of error for the running version:

• PBs from different periods. If the 1500 m PB is from your college days and the 5000 m PB is from last month, those two points can’t be placed on the same line.
• Insufficient distance spread. If you use 3000 m and 5000 m, the two points are too close, and the slope is unstable. Using 800 m brings in too much neuromuscular influence.
• Terrain and environment. One race on a flat track, another on a rolling road course; one in cool winter weather, another on a humid Taiwan summer morning—these differences get written directly into your CS.
• Pacing strategy. If you got disrupted mid-race, went out too fast and faded, that result doesn’t represent your true ability for that distance.
• Trail and hilly running can’t be plugged in directly. Speed is dominated by terrain; the CS concept only makes sense using “equivalent flat speed” or another quantification method.

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5. What Exactly Is W′: Physiological Meaning and Its Controversies

5-1 The Old View: Treating W′ as “Anaerobic Capacity”

The early intuitive explanation was: CP represents the upper limit of the aerobic system, and W′ is “the total capacity of the anaerobic system”—the phosphocreatine (PCr) store plus the total energy from anaerobic glycolysis. This explanation is easy to remember, but it’s now widely considered oversimplified and even misleading.

5-2 The Currently More Accepted View

A more reasonable understanding of W′ is: it’s a composite indicator of “how much internal environmental disturbance you can tolerate,” rather than a simple energy store. The relevant factors are thought to include:

• Phosphocreatine (PCr) depletion: PCr drops rapidly at high intensity, and the degree of PCr depletion is highly correlated with sustainable time.
• Contribution of anaerobic glycolysis: It produces ATP but also produces metabolic byproducts.
• Metabolite accumulation: Rising inorganic phosphate (Pi), acidification from hydrogen ions (H⁺), and extracellular potassium (K⁺) accumulation are all thought to interfere with muscle excitation–contraction coupling and force production.
• Interaction between central and peripheral fatigue: A deteriorating peripheral environment feeds back to the central nervous system, altering the regulation of exercise output.

In other words: W′ running low is more like “the internal environment has been pushed to some limit state” than “the fuel tank is empty.” This also explains why when W′ is exhausted, you’re not completely unable to move—you just “can no longer hold that intensity”—you’re forced back below CP.

5-3 W′ Is Not a Constant

This is very important in practice:

• It changes with training. Repeated short high-intensity training typically raises W′; large volumes of low-intensity aerobic training mainly act on CP.
• It’s compressed by fatigue. After consecutive days of high intensity or poor sleep, the same test often can’t produce your usual W′.
• It’s affected by prior exercise. An all-out effort done after two hours of riding usually yields less W′ than when fully rested.
• It’s affected by environment. In high heat and humidity, or in a dehydrated state, both W′ and CP can be revised downward.
• It’s affected by “daily form.” This sounds unscientific, but anyone with experience knows that two all-out tests in the same week can differ by an infuriating amount.

5-4 The Problem with the Linear Recharge Assumption

For the W′ balance model to work, it must answer “how fast does W′ come back when you’re below CP.” The simplest version assumes the recharge rate is proportional to “how far you are below CP”—if you’re 100 W below CP, you recharge twice as fast as if you’re 50 W below.

But actual observations generally suggest:

• Recharge is closer to exponential decay—fast at first, slower as you approach full.
• The closer you are to CP, the slower the recharge, and slower than the linear assumption predicts. In other words, “resting” at CP minus 10 W is far less efficient at recharging than you’d think.
• The deeper W′ is depleted, the slower the recharge. Refilling quickly after draining the bucket to the bottom is much harder than topping up after a shallow use.
• The recharge rate itself varies between individuals, and it also slows down in the same person under fatigue.

Practical conclusion: The W′ balance shown on your head unit is likely more optimistic than reality. When you see “back to 80%,” treat it as “recovered somewhat,” not “I have 80% of my bullets to spend again.”

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6. Race Pacing: Where This Model’s Real Value Lies

This is the most practically valuable chapter in the entire article. CP/W′ is worth learning not because the math is elegant, but because it turns “pacing” from mysticism into something you can reason about.

6-1 W′ Balance and Real-Time Display on Your Head Unit

Many head units and training apps now support a W′ balance (often written as W′bal) field: enter your CP and W′, and it calculates in real time “how much is left in the bucket.”

How to use it correctly:

• Treat it as a direction indicator, not a fuel gauge. It tells you “am I spending or saving right now” and “roughly what proportion have I spent,” not precise joules.
• Watch the slope of the trend. Dropping fast means you’re well above CP; a slow decline means you’re only slightly over; flat means you’re near CP.
• Set your own red line. Everyone has a different tolerance for “how much is left and can I still recover.” Some people start falling apart at 30% remaining; others can go very low and still come back. Learning your own red line through training matters more than trusting the number on the screen.
• Reviewing it after the race is more valuable than staring at it during the race. When you lay out the W′bal curve afterward, you’ll see clearly “which decision spent too much.”

When it’s unreliable:

• When the CP/W′ parameters themselves are poorly measured, the entire curve is wrong.
• In the later stages of long events (CP has already declined, but the model is still calculating with rested CP), it will seriously overestimate your remaining ability.
• In heat, dehydration, or fueling failure, the model has no way to account for these factors.
• Recharge is overestimated (see 5-4); the more “sprint—coast—sprint” the race pattern, the more error accumulates.

6-2 The Cost of Going Out Hard at the Start

When the starting gun goes off, adrenaline makes people do things they’d never agree to before the race.

Let’s calculate with hypothetical numbers (fictional example values below): a cyclist with CP 250 W and W′ 20 kJ averages 330 W for the first two minutes fighting for position:

• Above CP: 330 − 250 = 80 W
• Spent: 80 × 120 seconds = 9,600 J = 9.6 kJ, nearly half the entire bucket

And in those two minutes, the actual “extra distance” gained is very limited. Worse, he now has to ride at clearly below CP for a while just to get some of the bucket back; if he chooses to keep riding near CP, that 9.6 kJ is almost unrecoverable, and when he truly needs it later, the bucket is empty.

This is what “going out too hard” looks like mathematically: you buy a few dozen meters at a high price, then find the magazine empty when you need bullets most.

Practical advice: treat the first few minutes after the start as the highest-cost, lowest-return period. Unless your race strategy explicitly requires a certain position (e.g., in a criterium where early position determines whether you can save energy all race), there’s no reason to spend W′ there.

6-3 Drafting: The Cheapest W′ Recharge

The power saved by drafting is well known (how much depends on speed, formation, wind, and distance between riders; no precise numbers here). But in the CP/W′ framework, the value of drafting can be stated more precisely:

Drafting isn’t just “saving energy”—it’s the tool that pulls you from the “W′ spending zone” back into the “W′ recharging zone.”

At the same 30 km/h in a group: the rider on the front may be above CP, with the bucket leaking; the rider behind may be below CP, with the bucket recharging. Two people doing the same thing—one is spending, the other is saving. An hour later, their available resources are worlds apart.

Practical applications:

• Flat and headwind sections are where drafting has the highest value, and where you should most resist taking a turn on the front.
• The length of your pulls in a rotating paceline should be decided by “how much W′ do I have left,” not by pride. Short, frequent rotations usually maintain overall speed better than long, hard pulls.
• On climbs, the aerodynamic benefit of drafting drops dramatically (low speed), so “drafting” on climbs is mainly psychological and helps with rhythm—don’t expect the same energy savings.
• Safety reminder: The closer you draft, the better the benefit, but the higher the risk. Only draft closely behind riders you trust, and always stay within a distance where you can react. On open roads, prioritize a safe distance; don’t glue yourself to a wheel just to save W′.

6-4 Short Steep Climbs (Punchy Climbs): Where You Bleed the Most

Taiwan’s riding environment is full of these: a short steep pitch that kicks up after a flat section, a rise out of a corner, the ramp onto a bridge from the riverside path.

Calculated with hypothetical numbers (fictional example values): a cyclist with CP 250 W and W′ 20 kJ faces a steep climb that takes 1 minute.

Strategy	Average Power	Above CP	W′ Spent	Share of Full Bucket
Fighting to follow others	400 W	150 W	9,000 J	45%
Backing off a little	340 W	90 W	5,400 J	27%
Own pace	300 W	50 W	3,000 J	15%
Fully conservative	270 W	20 W	1,200 J	6%

The difference is striking. For the same one-minute climb, fighting hard costs three times as much W′ as riding your own pace. And the time difference between those three strategies over that minute is often only ten to twenty seconds.

The key decision here is: is the time difference on this climb worth that much W′?

• If there’s still a whole race ahead → almost never worth it.
• If getting dropped means you’re out of the race (group race), then it might be worth it, because “staying with the group” will save far more W′ later than this expenditure. This is an investment, not an expense.
• If it’s time-trial-like and there’s no group to draft afterward → ride your own pace; don’t perform.

The actual feel of a route like Fengguizui is exactly this principle: it’s not one continuous climb but a route with changing rhythm. Many people fight on the first few steep sections, spend most of the bucket, and only then realize the road is still long.

6-5 Criteriums and Team Races: Managing Repeated Sprints and Recharges

Criteriums are where the CP/W′ model shines most, because the power output is inherently sawtooth-shaped: accelerate out of every corner, reposition with every change in the group, follow every attack.

Calculated with hypothetical numbers (fictional example values): CP 250 W, W′ 20 kJ, a 20-lap criterium where each corner exit and reposition costs an average of 1.5 kJ:

• Total demand: 1.5 × 20 = 30 kJ
• But your entire bucket is only 20 kJ

The conclusion is clear: this race cannot be finished on the “initial 20 kJ” alone; you must continuously recharge between laps. So the key to winning a criterium is often not “how strong is your sprint,” but:

1. Cost control on each acceleration. Starting your acceleration earlier out of the corner (over a longer time with lower excess power) is much cheaper than waiting until the exit and surging hard. To bring speed back up, the lower the power peak and the longer the time, the less W′ is spent (because spending = excess × time, but the level of excess directly determines the burn rate per unit time).
2. Position determines cost. In the middle or back of the group, you have to re-accelerate at every corner (the accordion effect); at the front, speed changes are much smoother. Good position is the most effective way to save W′.
3. Seizing recharge windows. When you’re behind someone on a straight, actively confirm you’re actually below CP. Many people think they’re resting when they’re just “not in as much pain”—their power is still above CP. That’s slowly leaking, not recharging.
4. How much to save for the final sprint? This is the hardest judgment call. In principle: the W′ needed for a sprint depends on how long you plan to sprint and at what excess power. If your sprint habit is 15 seconds at ~700 W above CP (fictional example value), that’s 700 × 15 = 10,500 J, more than half the bucket. That means you must keep more than half your W′ for the entire race to have anything to fight with. For most people, this means you must start refusing all unnecessary efforts in the last five laps.
5. Recharging after a pull. After your turn on the front, drop back to the tail—don’t immediately try to move forward again. That time falling to the back of the group is your most important recharge window. But note: dropping all the way to the back means you’ll pay the accordion-effect cost on the next acceleration. This is a classic trade-off—drop too far back and you recharge more but the next acceleration is more expensive; stay too far forward and you recharge less but accelerate cheaper. In experience, most people choose to drop to the middle-front of the group rather than the very tail.

6-6 Individual Time Trials (TT): Why Variable Pacing Makes Sense

Intuitively, a time trial should be ridden at “perfectly even power” because that’s most efficient. But the CP/W′ model (and basic physics) tells us that on courses with rolling terrain or changing wind, moderate variable pacing is actually faster.

The reasons come in two layers:

Physical layer: Spending a little extra power where you’re slow (climbs, headwinds) buys more time savings than spending the same power where you’re fast (descents, tailwinds). Because aerodynamic drag roughly eats power with the cube of speed, adding watts at high speed has poor marginal returns.

Physiological layer (this is where W′ comes in): “Extra power spent” isn’t free; it comes from W′. But the whole point of W′ is that it can be spent. As long as you arrange W′ spending and recharging across the whole effort so that it hits empty exactly at the finish—not before—you’ve fully used all your resources.

The riverside flat time trial example: Taiwan’s riverside bike paths are where many people do time trials. They look flat, but there are wind direction changes, underpass ramps, and turns. A sensible approach: allow yourself to go slightly above CP on headwind sections and ramp climbs, and clearly drop below CP on tailwind sections and descending ramps to recharge. This is usually faster than “staring at the same wattage the whole way.”

But be warned about the risks of excessive variability:

• Too much variation will drain W′ early. Every time you go over the line, you’re being charged; charge too many times, too deeply, and you can’t recover.
• Recharge efficiency after deep depletion is poor (see 5-4), so a “big swings” strategy is physiologically more expensive than the model predicts.
• High variability accumulates extra fatigue, especially over longer distances.
• Practical principle: Treat variable pacing as “small oscillations around CP,” not “interval training.” In most cases, going slightly above target power on climbs and into headwinds, and slightly below on descents and tailwinds, is enough—you don’t need dramatic power spikes.

6-7 Long Climbs (Like Wuling): W′ Barely Matters

This is a key point many people haven’t thought through.

Calculated with hypothetical numbers (fictional example values): a cyclist with CP 250 W and W′ 20 kJ takes on a long climb requiring about 3 hours (10,800 seconds). Suppose he plans to spread W′ evenly across the entire climb:

• 20,000 J ÷ 10,800 sec ≈ 1.85 W

Spreading the entire bucket over three hours raises your average power by less than 2 watts. This is why on a sustained climb like Wuling—long duration, almost no downhill recharge opportunities—W′ contributes almost nothing to your result.

So what matters?

1. CP itself. How big your faucet is directly determines the intensity you can sustain for three hours.
2. Durability. That is, “how much of your CP is left after two hours of riding.” On a long climb, this may be as important as your rested CP value (detailed in Chapter 7).
3. Pacing discipline. If you go above CP on the early steep sections because “you feel great,” those expenditures are nearly impossible to recover later (since you’re climbing the whole time, there are no recharge windows). On a long climb, going over the line is a one-way street.
4. Fueling and body temperature. Over three hours, energy and hydration management directly determine how much ability remains in the later stages.

Practical advice: When tackling a long climb, save W′ for places where it’s truly necessary—for example, a few sections that are exceptionally steep where you’d stall out if you didn’t add pressure, or a short section of poor road you need to get through quickly. At all other times, keep power below CP and ride with the mindset of “infinitely sustainable”—that’s the right approach.

Also note: environmental conditions vary greatly on long climbs. Taiwan’s high-altitude sections have dramatic temperature swings, and body heat is lost quickly on descents—be sure to carry enough warm clothing. Descents are absolutely not a place to chase data; ride with a full margin of safety.

6-8 Beiyi and Long Rolling Routes: Designing Recharge Windows

Routes like Beiyi—“up and down, with climbs and descents”—sit between criteriums and pure climbs. Their defining feature is: there are clear recharge windows (descents, gentle downhills), but also multiple spending opportunities (every climb).

Pacing approach:

• Divide the route into “spending segments” and “recharge segments” in advance. Look at the profile beforehand and mark which climbs require going over the line and which descents allow true relaxation.
• Don’t go over the line on every climb. This is the most common mistake—thinking “there’s a downhill to rest on later,” so you spend a little on each one, and the accumulation far exceeds the recharge rate.
• Note that a descent isn’t necessarily a recharge. If you’re still pedaling hard on the descent (to maintain speed or follow someone), that’s not rest. True recharge requires power clearly below CP.
• Safety first: Descents on rolling routes usually come with corners and gradient changes. On descents, completely abandon evaluating yourself with power or speed data; road conditions, visibility, and braking distance always take priority.

6-9 The Running Version: Race Applications of CS and D′

Going out too fast: In running, bleeding at the start is even more common than cycling, because speed differences are less noticeable. Calculated with hypothetical numbers (fictional example values): a runner with CS corresponding to 4:06/km and D′ of about 280 m runs the first kilometer in 3:50:

• That’s about 16 seconds per kilometer faster, meaning in that kilometer he “ran extra” roughly 60 meters’ worth of D′ (rough estimate from speed difference × time)
• The very first kilometer eats more than one-fifth of D′

And runners usually don’t just run one fast kilometer—often the first three are all too fast. This is why “the first half feels easy, the second half falls apart” is the classic road-running failure mode—what you spend in the front half is the only lifeline you have for the back half.

Hilly road races: Many Taiwan races include bridges and uphill sections. The principle is the same as short steep climbs on the bike: on climbs, maintain “equal effort,” not “equal pace.” Forcing flat-ground pace on an uphill means spending D′ over the line. The sensible approach is to allow pace to drop on climbs and let speed come back naturally on descents (but don’t lose control on descents chasing speed—that’s the highest injury-risk place).

The final 400-meter sprint: This is the most legitimate use of D′—spend whatever’s left right before the finish line. The ideal race is “crossing the line at the same moment D′ hits zero.” Too many people finish with energy left, meaning the pacing was too conservative; too many people fade in the last 2 km, meaning D′ ran out long before.

Trail running short steep climbs: Trail terrain makes speed meaningless (the same effort on a steep slope might produce only a third of the speed on flat ground). In this case, the “speed” form of CS/D′ doesn’t apply, but the concept still holds completely:

• On short steep climbs, walking is usually far cheaper than forcing a run. Running hard up a steep slope is a classic high-cost D′ expenditure, and the time difference may be tiny.
• Technical descents are not recharge segments, because eccentric muscle load is high; even if heart rate drops, fatigue is still accumulating.
• Trail runners should manage with perceived effort (RPE) and breathing rhythm rather than staring at pace.

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7. Limitations of the Model: Don’t Treat W′ Balance as a Precise Fuel Gauge

7-1 CP Declines Over Time: Durability

This is the biggest hole in the two-parameter model. The model assumes CP is a fixed value, but over hours of activity, CP almost certainly declines.

After three hours of riding, your “infinitely sustainable power” is not equal to the CP measured when fully rested. This phenomenon is often called durability, or “decline in power performance after fatigue.”

Practical impact:

• The W′bal on your head unit will seriously mislead you in the later stages of a long event. It uses rested CP, so it thinks you’re still below CP and recharging, but in reality you may already be above (the declined) CP, leaking the whole time.
• This explains the common experience of “the numbers look fine, but the body is done.”
• Two cyclists with the same CP can have very different durability. One does lots of long endurance training; the other only does short sessions. Their performances on a three-hour climb like Wuling will be completely different—this difference is completely invisible in the two numbers CP and W′.

7-2 Other Things the Model Doesn’t Include

Factor Not Included	Actual Impact
High heat and humidity	Taiwan summer’s most real enemy. Cardiovascular drift, rising body temperature, and dehydration all lower sustainable intensity; the model has no idea
Nutrition and fueling	Carbohydrate intake during long events directly affects later performance; when fueling fails, both W′ and CP collapse
Position and aerodynamic drag	The model calculates “power,” but races are won on “speed.” Getting lower might save more than weeks of training
Muscle damage and eccentric load	Muscle damage from long descents or trail running isn’t in the energy model
Sleep and psychological stress	Directly affect the CP and W′ you can express on a given day
Equipment and road surface	Rolling resistance, tire pressure, and road quality all affect speed at the same power
Altitude	Usable aerobic power drops at altitude, especially in the later stages of Wuling
Technical efficiency	Especially in running and trail, economy differences can overwhelm the model’s predictions

7-3 The Right Mindset

Treat CP/W′ as “a useful pair of glasses with imprecise prescription”: it lets you see clearly what was blurry before (the cost of intensity accumulates, going over the line has a price, recharging requires true relaxation), but you don’t assume you can see molecules just because you’re wearing glasses.

The best practical use is:

1. Use it to build decision principles (e.g., “don’t fight on short climbs,” “don’t spend in the first three minutes,” “save half the bucket before the final sprint”).
2. Use it for post-race analysis (see which segment’s spending wasn’t worth it).
3. Don’t be held hostage by the number on the screen during a race; subjective feel (RPE) remains the most important real-time signal, especially in heat or long events.

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8. How to Train CP and W′

All content below is general training principles. Individual variation is huge, and progression must be gradual. Any new high-intensity training should be built on sufficient aerobic base and an injury-free state; if you have health concerns, chronic conditions, or have been inactive for a long time, consult a medical or sports professional before starting.

8-1 Raising CP (Opening the Faucet Wider)

CP essentially reflects the upper limit of aerobic energy supply and the ability to clear metabolites, so the training direction is:

• Aerobic base volume. This is the least glamorous but most effective part. Large volumes of low-intensity endurance riding/running work on mitochondria, capillary density, fat metabolism, and overall fatigue tolerance. Without a base, anything built on top collapses.
• Threshold-intensity training. Sustained or segmented training near or slightly below CP (e.g., long tempo segments with short recoveries). The goal is to increase “how long you can hold this intensity.”
• VO2max-intensity training. Repeated efforts clearly above CP (each segment a few minutes, with full recovery between sets). This spends W′, but long-term it pushes the ceiling of CP upward.
• Durability training (easily overlooked). If your goal is a long event like Wuling, having a high rested CP isn’t enough. Place threshold or VO2max segments in the later part of a long ride to train “the ability to output while fatigued”—this is the most direct way to improve durability. (These sessions are very demanding; ensure adequate recovery and introduce them progressively.)

8-2 Raising W′ (Making the Bucket Bigger)

W′ corresponds to short-duration high-intensity tolerance and neuromuscular ability:

• Repeated short high-intensity efforts. Each segment from ten-odd seconds to one or two minutes, clearly above CP, with sufficiently long recovery between efforts so each one is truly high quality.
• Repeated sprint ability (RSA) training. Short sprints with incomplete recovery, repeated many times. This is closer to the actual demands of a criterium—not “how strong is one sprint,” but “how much is left after ten sprints.”
• Neuromuscular/power training. Very short maximal efforts, low-cadence high-torque work, and strength training if needed.
• Strength training. Helps sprint ability and fatigue resistance, and also aids injury prevention.

8-3 There’s Often a Trade-off

This is the part many people aren’t mentally prepared for: CP and W′ cannot both grow infinitely at the same time.

Training Phase	Main Content	Typical Parameter Changes
Large base phase	Mostly low intensity, some threshold	CP rises slowly; W′ may stay flat or drop slightly
High-intensity phase	VO2max/short sprints	W′ rises clearly; CP may also rise but to a limited degree
Taper	Volume reduced, a few high-intensity stimuli kept	Both usually rebound; the “freshness” effect
Overtraining	Too much intensity and volume	Both drop simultaneously—this is a warning sign

Practical implications:

• First determine what your goal requires. Someone training for Wuling who spends time on sprint training is investing in something with almost no return (see 6-7); a criterium racer who only does long low-intensity rides will be drained on every acceleration.
• A season can’t have everything at maximum. Periodization to separate priorities is more realistic than chasing both goals at once.
• W′ dropping isn’t necessarily bad. In a base phase, W′ drops slightly but CP rises—that’s a good trade for long-distance goals. When looking at numbers, ask which one you need.
• If both drop at once, be alert. That usually means insufficient recovery; the answer is to reduce volume, not add more.

9. Summary of Common Mistakes

1. Plugging CP directly into the FTP field. Training zones get pushed higher overall, long-term training quality declines, and you think you’re not trying hard enough.
2. Fitting with a contaminated power curve. You’ve never seriously done a 3-minute all-out, yet you fit CP from the power curve, then complain the numbers are inaccurate.
3. Doing all three test stages on the same day. What you get isn’t CP; it’s “your fatigue curve.”
4. Fully trusting the real-time W′bal number. Especially after three hours, in extreme heat, or when fueling has failed.
5. Thinking “it doesn’t hurt that much” means you’re recharging. True recharge requires power clearly below CP, not “slightly more comfortable.”
6. Fighting for pride on short steep climbs. Ten-odd seconds of time difference for half the W′ bucket.
7. Still thinking about W′ strategy on a long climb. On a three-hour climb, the whole bucket is worth less than 2 watts (see 6-7); what you should think about is CP and durability.
8. Chasing data on descents. This is the highest-risk mistake of all. No pacing optimization is worth trading for safety.
9. Inconsistent conditions between tests. Changed trainer, changed power meter, changed season, changed time window, then comparing numbers and claiming improvement.
10. Forcing a test despite poor daily condition. Poor sleep, early-stage cold, or just back from a business trip, then doing a maximal test, getting a bad number, and doubting yourself. If your body isn’t right, do it another day—that’s discipline, not laziness.

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10. Action Checklist: What to Do Starting Today

Step 1: First Confirm Whether You Need It

• If you only do long-distance endurance riding or road races of marathon distance or longer, honestly, W′ has limited impact on your results. Put your effort into CP and durability.
• If you do criteriums, hill climbs, rolling-terrain races, road races with sprints, or trail running, then understanding W′ will directly change how you race.

Step 2: Obtain Usable Parameters

1. Do a health assessment first. Any cardiovascular concerns, chronic conditions, or long-term inactivity—consult a physician first.
2. Choose one method and stick with it. It’s recommended to start with multi-stage all-out testing on separate days (with durations spread apart).
3. Use the same device, venue, and conditions for every test.
4. Record the method and date clearly so future comparisons are meaningful.
5. Make sure the test location is safe: prioritize a trainer or closed course; if outdoors, choose roads with minimal traffic, good pavement, and no intersections, and avoid rush hour and wet weather. Don’t race on open roads.

Step 3: Turn the Numbers into Three Race Rules

Write down three rules of your own, for example:

1. Don’t spend W′ in the first 3 minutes after the start (unless strategy requires fighting for position).
2. On short steep climbs, ride your own pace, don’t fight others (unless getting dropped means you’re out).
3. Save enough allowance before the final sprint (estimate how much you need based on your own sprint habits).

Step 4: Verify with Post-Race Analysis, Not by Staring During the Race

• After the race, lay out the W′bal curve and find the segments where spending “wasn’t worth it.”
• Record the gap between subjective feel and the numbers, and calibrate where your own red line is.
• After accumulating data from three to five races, your understanding of your own bucket will be more accurate than any model.

Step 5: Make Trade-offs in Training

• Clearly define your primary goal, and use it to decide whether this season is about CP, W′, or durability.
• Don’t skip the low-intensity base.
• Introduce high-intensity sessions progressively; if both parameters drop at once, reduce volume.
• Individual variation is huge; don’t copy someone else’s plan.

Finally, Three Takeaways

• CP is your faucet, W′ is your bucket—know which one each race is testing.
• Every watt and every second above CP is a charge, and recharge is slower than you think.
• The model is for building judgment, not replacing it; your body’s signals, the weather, road conditions, and safety always come before the numbers.

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Disclaimer: This article is a general sharing of training and pacing information. It does not constitute medical advice and cannot replace evaluation of your individual situation by a physician or sports medicine professional. High-intensity maximal testing carries cardiovascular risk; confirm your health status before proceeding, and stop immediately and seek help if you experience any discomfort during exercise. All training recommendations vary greatly between individuals; progress gradually. For outdoor riding and running, obey traffic rules and pay attention to environmental safety. This site does not encourage racing behavior on open roads.

Related Reading

• Critical Power (CP) vs FTP: Which Is Your Real Threshold?
• Critical Power and W’: The Two-Parameter Model Explaining How Long You Can Last
• FTP and the W’ Balance Model: Why Only Looking at FTP Makes You Lose Attack-Based Races
• The Critical Power CP Model: A Framework with More Explanatory Power Than FTP