ENGINEERINGSection 4.10.48 · Building 10 · ELUSK · College X · Engineering · ELUSKPier scour analysis — Horseshoe vortex geometry, HEC-18 §7.2, four pier nose shapes, post-peak backfill. Lester Pearson, PE.
Honest flag — who built this.Lester Pearson, PE is a fictional character — not a real licensed engineer, and he holds no license in any jurisdiction. The working tools this lab draws on are built by Travis Jenkins, EIT, a Transportation Hydraulic Specialist at TDOT, on personal time. The science and the sources are real; the people are not.
≋ Engineering · College X · ELUSK
The Horseshoe Vortex
Pier scour analysis — horseshoe vortex geometry, HEC-18 §7.2, four pier nose shapes, post-peak backfill. Lester Pearson, PE.
A browser hydraulics lab. Top-down channel, a pier in the middle, flow moving left to right. You pick the pier nose shape, the bed material, and the flow. The lab computes the pier scour depth using the HEC-18 §7.2 equation — the same equation TDOT, FHWA, and every state DOT uses to evaluate scour-critical bridges — and shows you the horseshoe vortex that does the actual gouging.
v0.4 additions (post-boss feedback): every slider now has a number-input box (type the exact value you want). Wall pier added as a fourth nose shape. Angle of attack θ (HEC-18 K₂) drives the scour-depth multiplier when stream lateral migration attacks the pier off-axis after construction — try Wall at θ = 30° and watch what happens. ▶ Play button animates Time T from pre-event through peak to post-event recovery; Backfill slider controls how much of the peak scour refills on the falling limb of the hydrograph (default 20%; tunable 0–40%).
The same vortex shows up somewhere else
The horseshoe vortex is not unique to hydraulics. The same flow pattern forms at the tip of every finite aircraft wing — two counter-rotating tubes of air trailing behind the wingtips, the visible signature of how lift is generated. This lab is the water-and-piers half of the story; the aircraft-wing companion lives at The Wing — Lift, Vortices, and What the Brothers Found. Both sit in the OPA Engineering Suite next to each other on purpose: same physics, two professions that don't usually talk to each other.
The hidden lesson
Pier scour is not caused by water hitting the pier. It is caused by the rotating vortex that wraps around the base of the pier perpendicular to the flow, sucking sediment out from underneath. The Horseshoe Vortex. You can see why a sharp nose buys you ~18% less scour than a square one even though the flow is identical — the wedge disrupts the vortex before it can fully form.
The Three Gauge Test
The matrix scorecard on the right is the lab's version of Lester Pearson's Three Gauge Test. One run is faith. Two runs is comparison. Three runs is verification. The insight panel stays locked until you've logged at least three independent configurations — varying shape, substrate, or flow. The instrument refuses to teach you the pattern until you've earned the right to read it.
What is and isn't here
The HEC-18 K₁ (pier nose shape) coefficients are the actual production values from ScourPulse, the professional tool. K₄ (substrate D₅₀) here is a simplified D₅₀-only version — the full HEC-18 K₄ is velocity-dependent. The flow field around the pier is a simplified potential-flow + wake approximation — physically faithful in shape, not calibrated to a specific Reynolds number. The scour hole is rendered at the equilibrium HEC-18 depth, not time-stepped through development.
The lab teaches the shape of pier scour. For design work, use ScourPulse or HEC-RAS proper.
Suite context
Lab of the OPA Engineering Suite · Sibling to the Browser Physics Suite (Chladni, Acoustic Levitation, Ripple Tank, Double-Slit, Edge Cases) and the Philosophy Suite (The Standing Question). Filed under College X (Engineering), ELUSK Building 10, Opathorlokan University, Birmingham, Alabama.
Course anchor: HYDR 250 (Lester Pearson · HEC-RAS Flood Modeling). Cross-listed with CIVL 155 (Hydrology & GFAS) and section 4.10.34 (Federal Flood Data Audit Methodology / Teach the Teachers).
Built by Travis Jenkins (User Zero) with Claude. The instrument exists because we didn't have nothing at UT Martin, and somewhere right now there's a hydrology student who needs to see the vortex form before the math will hold.
Lester's lectern
The Pearson register
The first time Lester Pearson stood in a classroom at the ELUSK Building, he set his yellow legal pad on the lectern, set a foamy 44-ounce Jose's next to it, and let the room watch him do nothing for forty-three seconds. Then he said:
"Believe the water."
He turned to the whiteboard and wrote three words at the top: The Legibility Problem. Underlined twice. Then he turned back:
"Most of what I'm going to teach you, you're going to disagree with the first time. The second time, you're going to say it's obvious. The third time, you're going to wonder why nobody told you sooner. The job is to get you to the third time before the next major flood happens. Let's go."
What this lab carries from his classroom
Believe the water. The visualization is the apparatus. Don't trust the K₁ number until you've seen the vortex change shape.
The Three Gauge Test. One run is faith. Two is comparison. Three is verification. The matrix scorecard refuses to teach you the pattern until you've earned the right to read it.
The conservative default is the agency's number, not yours. Square nose at K₁=1.1 is what your boss specs because the conservative number protects the agency. The lab opens square because that's the default in the field. Try the sharp nose. Ask yourself which one you'd put on a bridge your kid drives over.
Some things you fix. Some bugs you let bug. Riprap on a new pier is a bug FHWA tells you to fix (don't put it there). Riprap on an already-scoured existing bridge is sometimes a bug you let bug, because there is no other option. The skill is knowing which is which.
The flickering fluorescent in the corner of the canvas
The fluorescent above Lester's lectern in ELUSK Building 10 has been flickering since the building opened in 1972. The lab carries it — top-right corner of the canvas. Some flickers you let flicker.
Required reading
Nashville/lester_surge_tower.txt · Oct 2024 – Jan 2025 · Hurricane Helene, the I-40 Mile Marker 7 washout, the Pigeon River gauges, four AI failures in three days, the dyslexia-as-AI-defense origin of the Three Gauge Test.
4.10.34 OPA_ELUSK_FederalFloodDataAudit_LesterPearson_TeachTheTeachers.md · The textbook. This lab is its bench.
Sources & equations
The actual math under the hood
HEC-18 §7.2 — pier scour
Citation corrected 6 Sep 2026: this lab cited “HEC-18 §6” in six places. In the 5th Edition (FHWA-HIF-12-003, April 2012) Chapter 6 is Contraction Scour and Chapter 7 is Pier Scour; the equation below is §7.2. Verified against FHWA’s own PDF. The equation itself was right the whole time — only the pointer was off, and a pointer to the wrong chapter of the right manual is the kind of thing that survives review for years.
Federal Highway Administration, HEC-18 Evaluating Scour at Bridges, 5th Edition. The lab fixes K₂ = 1.0 (no skew, head-on flow) and K₃ = 1.1 (typical bed condition) so the student sees the K₁ (shape) and K₄ (substrate) effects without other variables muddying the result.
Sand and fine gravel (D₅₀ < 60 mm) get full scour. Coarser substrate armors the bed — the larger particles resist entrainment and partially shield finer material underneath. Cobble bed at D₅₀ = 128 mm gets K₄ ≈ 0.77.
Critical velocity Vc
Vc = 11.17 · y₁1/6 · (D₅₀ / 304.8)1/3
The threshold velocity above which the approach flow itself can move bed material. V₁ > Vc means live-bed scour (sediment supply from upstream, equilibrium scour depth). V₁ < Vc means clear-water scour (no supply, scour proceeds to maximum). The canvas overlay labels which regime you're in.
The horseshoe vortex itself
The visualization is a simplified representation of the secondary flow that forms at the upstream face of a pier in turbulent open-channel flow. Real horseshoe vortices wrap fully around the pier base, are reinforced by the downflow at the upstream stagnation point, and carry sediment downstream into the wake. The lab shows the upstream counter-rotating pair because that's where the gouging actually starts.
The overlay prints “Downflow on pier face” as a velocity in feet per second. That figure is 0.65 × the approach velocity, and you should know what it is and is not. It is a modelling constant this lab chose, attributed to Melville & Coleman (2000). It is not a measurement, and it is not a value this project has been able to confirm in a primary source.
Eleven sources have now been searched for it and come back empty — nine papers and databases on disk, plus two FHWA hydraulics research pages. Every mention of downflow in the set is qualitative: the mechanism, never a coefficient. Two of those misses explain the rest:
The field normalises downflow against itself, not against the approach flow. Unger & Hager (2007) — the one study that measures downflow directly, by PIV, inside a developing scour hole — define their normalised downflow as Vzf = vzf / vzf,max. They define the approach velocity Vo and use it in three dimensionless groups, but never as the denominator for downflow. A “fraction of approach velocity” is simply not a quantity their framework produces.
And the big field database does not record downflow at all. USGS Data Series 845 compiles 2,427 field and laboratory measurements of pier scour. Its variables are pier width, approach velocity, flow depth, median grain size and scour depth — the inputs and the outcome. Not one of the 2,427 records the downflow. The profession measures what the vortex does and skips what the vortex is.
So the number stays at 0.65 and stays labelled. Changing it to a different unsourced number would not be an improvement, and a published ratio would vary with pier width, approach depth and where in the column the maximum is taken. If you have Melville & Coleman open to the page, or institutional access to Experiments in Fluids 42(1), 1–19, the note in this page’s source code says exactly what would close it. Last searched 23 September 2026.
D₅₀ ≥ K · V² / [(Ss − 1) · 2g]
where K = 0.692 (round/cylindrical pier), 1.0 (square)
FHWA does not recommend riprap as a pier scour countermeasure on new bridges. The v2 module will allow placement on existing scour-critical bridges only — and will show the rocks plucking out one at a time above the Isbash velocity threshold, creating downstream secondary scour. That's the lived lesson from a week of class on riprap design: even sized right per DG-11, you're hoping and praying.
A note from the builder
Single developer. A 49‑year‑old father and solo builder.
If you see something wrong, please let me know — I’ll change it as soon as I can. I’ll credit you if you want the credit.
Some labs are better than others; a few have obvious broken bits I’m still working through. Some were built early, some late — they don’t all look the same, but they share a feel.