25 February 2026

Maths and Sailing: the Day I Discovered “Tacking” Is Basically Algebra With Wet Shoes

There are two kinds of people in the world: those who think maths is thrilling, and those who think it’s something that happens to other people in exam halls. Then there are sailors… who accidentally do maths all the time, usually while holding a rope and trying not to look panicked.

When you sail on a river (hello, Thames), you quickly realise you can’t just point at where you want to go and go there. The wind has other plans, the stream has very other plans, and the boat has the personality of a stubborn shopping trolley. So you tack — zig-zagging upwind — which is basically a real-life lesson in angles, vectors, and “Why isn’t this working the way it did on the whiteboard?”

1) Angles: “Close-hauled” is a geometry problem

Upwind sailing is all about the angle between the boat and the wind. Too close and the sail flaps like a sad flag. Too far off and you lose ground. That sweet spot? It’s the practical version of “find the optimal angle” — except your calculator is a tell-tale and your teacher is the wind shouting “NO.”

Classroom link: get students drawing angle diagrams with wind direction as a reference line, then ask: Which heading gives the fastest progress toward the buoy? It’s bearings and geometry with purpose.

2) Speed and distance: the river won’t wait for your calculations

Want to know if you’ll reach the mooring before the tide pins you sideways? That’s speed = distance ÷ time — but with a moving conveyor belt underneath you. On the Thames, “I’ll just glide in” turns into “Why am I drifting into Berkshire?”

Classroom link: real data problems: boat speed through water vs speed over ground. Give students two speeds and ask them to work out drift, time to a marker, or whether the boat arrives upstream or embarrassingly downstream.

3) Ratios and forces: the sail is a giant triangular maths lesson

Sail shape (and how tight you pull everything) affects speed. A flatter sail is different to a fuller one — and suddenly you’re in ratios, proportional reasoning, and “adjust this by a bit and the whole system changes.”

Classroom link: show a simple sail triangle and explore how changing one side (sheet tension, boom position) changes the “shape” and performance. You don’t need to go full physics — just proportional thinking and graphs.

4) Turning circles and pivot points: maths you can feel

Powerboaters learn that boats pivot in different places depending on forward or reverse. Dinghies do their own version when tacking and gybing — turn too fast and you stall; too slow and you drift. It’s all about rates of change in the real world.

Classroom link: graph “heading vs time” during a tack and discuss steep vs gentle slopes. Suddenly gradients mean something other than “that line goes up.”

5) Probability: will this tack work… or will I be doing an accidental three-point turn?

Every tack is a mini gamble: wind shift, gust, lull, other boats, and the dreaded “in irons.” That’s probability, decision-making, and risk — plus a splash of psychology.

Classroom link: simple tree diagrams: if wind shifts left/right, what’s the best choice? Add constraints like river width. This becomes a genuine “thinking problem” rather than a worksheet.

Making maths more interesting (without pretending it’s all fun)

The trick isn’t to say “maths is amazing!” while students stare back like you’ve suggested revising for fun. The trick is to give maths a job to do.

Sailing gives you a ready-made world where numbers matter:

If you get the angle wrong, you don’t reach the buoy.
If you misjudge time and drift, you miss the mooring (and your dignity).
If you don’t estimate properly, the river teaches you… repeatedly.

And the best part? Students who think they “aren’t maths people” often are — they just haven’t met maths in a form that moves, splashes, and occasionally shouts “LEEWARD!”

If you want to make maths more interesting, don’t add more gimmicks. Add more reasons. Ideally ones involving boats.

24 February 2026

Measuring the Speed of Sound in Water (without owning a submarine)

Measuring the speed of sound in air is a classic: two microphones, a clap, a ruler, and a small argument about who started the stopwatch too late. Water, however, is a different beast. Sound travels much faster in water than in air, so the time differences you’re trying to measure are tiny. That doesn’t make it impossible — it just means we need methods that don’t rely on someone’s thumb hovering over a phone timer like it’s the Olympic 100 m final.

Below are three practical approaches, from “school-lab achievable” to “this feels like we’re doing proper marine science”.

Method 1: Time-of-flight with two underwater microphones (best and most direct)

Idea

Send a sharp sound pulse through the water. Record when it arrives at two sensors a known distance apart. The speed is:

v = \frac{d}{\Delta t}

Where:

$d$ = distance between sensors (m)
$\Delta t$ = time delay between the two recordings (s)

What you need

A long water tank / trough / (in a pinch) a swimming pool
Two hydrophones (underwater microphones)
- If you don’t have hydrophones, you might hack it with waterproofed microphones in sealed bags, but reliability varies wildly.
Something to record both channels at once:
- A 2-channel audio interface into a laptop works brilliantly
- Some data loggers can do it too
A sharp sound source:
- Two pieces of wood tapped together underwater (clappers)
- An old school bell ( what we used)
- A short ultrasonic “ping” if you have a signal generator + transducer

Procedure

Mount the two hydrophones in line, separated by a measured distance (say 0.50 m to 2.00 m).
Make a sharp sound pulse near one end (closer to hydrophone A).
Record both traces.
Measure the time shift between the first big peak on channel A and channel B.
Calculate $v$ .

Tips to make it work

Use a bigger distance if you can.
Example: if $v \approx 1500\ \text{m s}^{-1}$ , then over 1.0 m the delay is only about 0.00067 s (0.67 ms). That’s measurable… but you need decent sampling.
Set audio sampling to ≥ 44.1 kHz (better: 96 kHz).
Keep sensors at the same depth to reduce odd paths and reflections.
Do it in the middle of the tank, away from walls, or you’ll get echoes bouncing about like a pinball machine.

Typical result

Fresh water at room temperature is usually around 1480–1500 m/s.

Main uncertainties / errors

Reflections from walls and the surface (extra peaks)
Distance measurement (especially if sensors aren’t truly in line)
Temperature (sound speed changes with temperature)

Method 2: Echo (SONAR-style) using a single sensor (simple concept, fiddlier in practice)

Idea

Make a sound pulse and measure the time until the echo returns from a reflecting surface at distance $L$ :

v = \frac{2L}{t}

Because the sound goes there and back.

What you need

A hydrophone (or transducer) and recorder
A flat reflecting target (a metal plate works well)
A way to know $L$ accurately

Procedure

Place the reflector at a known distance $L$ from the sound source/sensor.
Make a sharp pulse.
Measure the time to the echo peak.
Compute $v$ .

Why it’s trickier

Echoes can overlap with the original pulse in small tanks.
Multiple reflections can confuse which peak is “the” echo.
Works better in a long tank or a pool.

Method 3: Resonance in a water-filled tube (clever, but equipment-sensitive)

This is the “do it like the air resonance tube experiment… but underwater” approach.

Idea

Drive sound at a known frequency $f$ and find standing-wave positions in a column of water. Then:

v = f\lambda

If you can measure the wavelength $\lambda$ in water.

Challenge

Generating and detecting clean standing waves in water is harder than in air, and reflections/attenuation can be awkward. This is more of a “physics club project” than a quick GCSE practical — but it’s a brilliant extension activity if you have ultrasonics kit.

What to record in your results table

For time-of-flight (Method 1), a neat table looks like:

Sensor separation $d$ (m)
Time delay $\Delta t$ (s)
Calculated speed $v$ (m/s)
Water temperature (°C)
Notes on reflections / signal quality

Repeat for several distances and average the result.

Safety and sanity notes

Electricity + water: keep interfaces/laptops well away and use long leads.
Don’t smash glass tanks with enthusiastic spoon percussion.
If you use ultrasonics: it’s generally safe at typical lab levels, but don’t drive powerful transducers in a way that heats water or stresses equipment.

A nice “why it’s faster in water” paragraph (for the write-up)

Sound travels faster when particles are more strongly coupled (stiffer medium) and slower when the medium is more compressible. Water is far less compressible than air, so disturbances pass along more quickly — even though water is denser

23 February 2026

A-Level Biology: Is there much life in a river in late February / early March?

If you stand on a bridge in late February and declare, “This river is dead,” the river will respond by doing what rivers do best: quietly getting on with it while you look at the surface like it’s the whole story.

The big difference at this time of year isn’t whether there’s life, but where it’s hiding and how active it can be, which comes down to temperature, flow, light, and habitat.

1) What “late winter” does to river life (in general)

Late Feb/early March in the UK is usually:

Cold water → slower enzyme activity, slower metabolism, less visible animal movement.
Low light / low primary productivity → less algae and plant growth, so less grazing happening in plain sight.
Higher flows after rain (often) → animals shelter in margins, under stones, in weed beds, and in slower back-eddies.

So: fewer “wow” moments at the surface, but plenty happening below it.

2) Chalk stream River Gade: life with the thermostat left on

Chalk streams are groundwater-fed, so they tend to have clear water, stable flows, and relatively stable temperatures (often quoted around ~10 °C for groundwater-fed systems). That stability gives them longer growing seasons and supports lots of specialist invertebrates.

In late winter on a chalk stream like the Gade, you’re often more likely to find:

Active macroinvertebrate larvae/nymphs (mayflies, caddisflies, stoneflies—“riverflies”) tucked into gravel, weed, and margins.
Fish still feeding (not frantic, but not completely “switched off”), helped by that steadier temperature.
Clearer signs of habitat structure (gravels, ranunculus beds later in spring, undercut banks), which matters because habitat complexity = niches.

In other words: the Gade can look “quiet”, but it’s often quietly busy.

3) River Thames at Bourne End: bigger river, bigger hide-and-seek

The Thames at Bourne End is a larger, slower-to-warm (and often more turbid) lowland river reach. In late winter, you can still have huge biomass present, but it’s typically:

Deeper and dispersed (fish shoals holding in steadier water)
More influenced by flow events (spates can shift fine sediment and nudge invertebrates into refuges)
Less visibly “chalk-stream sparkly” because suspended particles reduce light penetration (so you see less plant/algal action until spring picks up)

But don’t confuse “less visible” with “less alive”: Thames catchment monitoring routinely records diverse macroinvertebrate and plant communities across the system, and seasonal sampling shows that invertebrate communities are there year-round.

4) So… which has “more life” in late Feb/early March?

If you mean most visible life on a quick look:

Chalk stream (Gade) often wins: clearer water + stable temperature = more obvious signs (and easier sampling success).

If you mean total biomass and variety of habitats:

Thames can be immense, but you need to sample smartly (margins, slack water, submerged structure) to “see” it.

A nice A-Level way to phrase it:

In late winter, chalk streams often show higher apparent activity and detectability, while large lowland rivers may have equal or greater biomass that is less detectable without targeted sampling.

5) A-Level fieldwork angle: how to test it (properly)

If you want students to compare Gade vs Thames in late winter, make it a mini investigation:

Standardised kick sample (same time, same net mesh, same number of kicks)
Record flow, temperature, dissolved oxygen, turbidity, substrate type, channel width/depth
Identify macroinvertebrates to family level and calculate a biodiversity index (e.g., Simpson’s)
Optional: focus on EPT groups (mayfly/stonefly/caddis) as a rough indicator set.

You’ll usually find the chalk stream produces “nicer” samples for beginners (cleaner, easier to sort), while the Thames rewards patience and better site choice.

6) A seasonal footnote: “Where are the fish?”

A lot of coarse fish spawning is typically spring/summer as temperatures rise, so late Feb/early March is often more about overwintering behaviour than spawning frenzy.

22 February 2026

Understanding Cash Flow (and why profitable businesses still go bust)

A and GCSE Business Studies

Cash flow is the movement of cash into and out of a firm’s bank account.
Profit is when revenue is greater than total costs.

Those two sentences look similar… right up until your “profitable” business can’t pay the rent on Friday.

Think of it like this:

Profit is your score (based on what you’ve earned and what you’ve incurred).
Cash flow is your oxygen (based on what has actually arrived in the bank, and what’s actually left it).

A business can “win on points” (profit) while still running out of oxygen (cash).

Why cash flow and profit don’t match

1) Timing: “Sold” doesn’t mean “paid”

You might invoice a customer today… but they might pay in 30, 60, or 90 days.

So your accounts may show a profitable sale, but your bank account is still doing its best impression of a tumbleweed.

Example:
You sell £10,000 worth of work in January on 60-day terms.
That’s great for profit in January… but the cash might not show up until March.

2) Cash leaves before you’ve “made” the sale

Businesses often pay for stock, wages, and rent before customers pay them.

That gap is where cash flow dramas live.

3) Non-cash costs affect profit (but not cash)

Some costs reduce profit without an immediate cash payment.

Depreciation is the classic: the value of equipment “wearing out” on paper.
The cash left the bank when you bought the kit, not each month afterwards.

So you can have:

Lower profit due to depreciation,
while cash flow that month looks fine.

4) Investment spending hurts cash flow (but not necessarily profit)

Buying a new van, refurbishing the shop, purchasing a 3D printer that you absolutely “need” (honestly)…
That’s a cash outflow now, even though the benefit is spread over years.

5) Loan repayments are cash outflows, but not all are “costs”

Repaying a loan:

Interest counts as a cost (affects profit),
Repaying the capital does not count as a cost, but it does reduce cash.

This catches students out all the time.

A simple cash flow example (the “how are we broke?” moment)

Imagine a small business in January:

Cash in:

Customers pay: £2,000

Cash out:

Rent: £1,200
Wages: £1,500
Stock purchase: £800

Net cash flow = £2,000 − (£1,200 + £1,500 + £800)
Net cash flow = £2,000 − £3,500 = –£1,500

So cash is falling.

But profit for January might look like this:

Sales made (invoiced): £6,000
Costs incurred: £4,000
Profit = £2,000

Profit: +£2,000
Cash flow: –£1,500

That’s how you can be profitable and panicking in the same month.

Why cash flow matters so much in Business Studies (and real life)

Cash flow problems can cause:

Late payments to suppliers (and damaged relationships)
Missed wages (and an instant morale collapse)
Emergency overdrafts (and extra costs)
In extreme cases: business failure, even when the business is “profitable”

In exams, you’ll often link this to:

Working capital (current assets − current liabilities)
Cash flow forecasting
Reasons for using finance (overdrafts, short-term loans)
Managing trade credit (both given and received)

Quick ways businesses improve cash flow

Increase cash inflows

Encourage faster customer payments (shorter credit terms)
Offer small discounts for early payment
Chase late invoices (politely at first… then less politely)
Take deposits or upfront payments

Reduce or delay cash outflows

Negotiate longer payment terms with suppliers
Reduce unnecessary spending
Manage stock levels (too much stock = cash sitting on shelves)
Lease rather than buy expensive assets (sometimes)

Mini “exam-ready” summary

Profit = revenue − total costs (measured over a period, includes non-cash items).
Cash flow = actual cash in − actual cash out (bank balance reality).
A business can be profitable but still fail if it can’t meet short-term payments.

21 February 2026

“Ask an AI to do extended thinking…” — and it tells you what it’s doing?! (Sort of.)

A Level Computing | Philip M Russell Ltd style | UK spelling

You’ve seen it happen:

You ask an AI a tricky question.
You click the button that says something like “extended thinking”.
And then—instead of just blurting out an answer like an overconfident Year 10—you get a response that sounds like the AI is narrating its brain:

“First I’ll break the problem down… then I’ll check edge cases… then I’ll verify…”

It feels like watching a student show their working. Which is oddly comforting.

But here’s the important bit for A Level Computing:

The AI isn’t “showing its thoughts” in the way you think

Most modern AI systems do not reveal their full internal reasoning (often called chain-of-thought). What you’re seeing is usually a summary of the approach: a tidy, human-readable explanation of the steps it took or would take.

That’s not a bad thing. In fact, for learning, it can be brilliant — but you need to understand what you’re getting.

What “extended thinking” usually means (in plain English)

When you request extended thinking, you’re generally asking the model to:

Spend more compute/time on reasoning
Break the task into sub-problems
Self-check for contradictions and missing cases
Explain the method more explicitly than usual

In A Level terms, it’s similar to switching from:

“Give me the answer”
to
“Show me your algorithm, and then run it carefully.”

Why it looks like the AI is narrating its process

Because narration is useful.

A well-structured explanation often includes:

Identifying inputs/outputs (specification thinking)
Planning a method (algorithm design)
Checking constraints (edge cases, assumptions)
Verifying results (testing / validation)

That’s basically the Computational Thinking toolkit:
Decomposition, abstraction, algorithmic thinking, evaluation.

So the AI is doing what your teacher has been nagging you to do all along. (Annoying, isn’t it?)

The catch: “explanations” are not the same as “proof”

Even if the AI gives you a lovely step-by-step explanation, it can still:

use a wrong assumption,
miss a constraint,
produce an answer that sounds correct but isn’t.

So treat it like a very fast study partner who sometimes confidently walks into lampposts.

A Level-friendly rule:

Use the AI’s explanation as a draft algorithm — then test it like you would test your own code.

How to prompt it properly (so it actually helps you learn)

Try these prompt styles:

1) Ask for a plan first (before the final answer)

Prompt:
“Give me a brief plan (like pseudocode / method) before the final answer.”

Why it helps: you can spot dodgy logic early.

2) Force it to state assumptions

Prompt:
“List your assumptions explicitly before solving.”

Why it helps: you can challenge the weak bits.

3) Ask it to check edge cases

Prompt:
“After answering, test your solution against 3 edge cases.”

Why it helps: that’s literally exam evaluation.

4) Ask for a marking-grid style response

Prompt:
“Answer like an A Level student: define terms, show method, give final result, then evaluate limitations.”

Why it helps: it mirrors how marks are awarded.

A quick example: “Explain how you’d search for the fastest route”

Instead of:
“Find the fastest route.”

Try:
“Explain how you’d approach this: identify the graph model, choose an algorithm, and justify it.”

Now you’re doing proper A Level:

Graph representation (nodes/edges/weights)
Algorithm choice (Dijkstra vs A* vs BFS)
Justification (constraints, complexity, correctness)

So… should you trust the “thinking”?

Trust it the way you trust a calculator:

Great for speed
Great for structure
Still your job to check it’s answering the right question

And if it gives you a neat method: brilliant. That’s basically revision.

Just don’t confuse “a convincing explanation” with “guaranteed correct”.

20 February 2026

A-Level Chemistry — Iodine and its Properties (the glamorous purple one)

If chlorine is the loud, attention-seeking halogen and bromine is the moody one, iodine is the dramatic artist: it sits there looking like a dull grey solid… then quietly produces a purple vapour that makes everyone in the lab suddenly pay attention.

This post is a tidy A-Level tour of iodine’s key physical and chemical properties, plus the bits exam questions love to poke.

1) Where iodine sits and what that tells you

Iodine is a Group 17 (halogen) element. Like the others, it exists as diatomic molecules: I₂.

Trends down Group 17 (F₂ → Cl₂ → Br₂ → I₂):

Melting/boiling points increase (bigger molecules → stronger intermolecular forces)
Colour gets darker
Reactivity decreases (harder to gain an electron as atoms get larger and shielding increases)

So iodine is less reactive than chlorine and bromine, but it still does plenty of chemistry.

2) Physical properties you can actually see

Appearance and state

Grey/black crystalline solid at room temperature
Produces a purple vapour when warmed

Sublimation (a favourite classroom moment)

Iodine can sublime: solid → gas without becoming a liquid first (under normal lab conditions).
That purple vapour is iodine gas (still I₂ molecules).

Why does iodine sublime easily?
Inside each I₂ molecule, the I–I covalent bond is strong. But between molecules the attractions are only London dispersion forces—and warming supplies enough energy to overcome those.

3) Solubility: iodine is fussy

Iodine is non-polar overall, so:

Low solubility in water
Much more soluble in non-polar solvents (e.g. cyclohexane / hexane)

Colour clue (classic practical / exam):

In water: brown/yellow-brown (a mixture of I₂ and some I₃⁻ if iodide is present)
In cyclohexane: vivid purple (I₂ really showing off)

If you add iodide ions (from KI), iodine forms triiodide:

$\mathrm{I_2(aq) + I^-(aq) \rightleftharpoons I_3^-(aq)}$

This helps “pull” iodine into aqueous solution.

4) Simple redox behaviour (the exam engine)

Iodine is an oxidising agent (it accepts electrons), but weaker than chlorine or bromine.

Reduction half-equation:

$\mathrm{I_2 + 2e^- \rightarrow 2I^-}$

That’s the backbone of loads of questions: titrations, displacement, and redox calculations.

5) Displacement reactions: who can bully whom?

A more reactive halogen displaces a less reactive one from its halide.

So:

Chlorine displaces iodide:

$\mathrm{Cl_2 + 2I^- \rightarrow 2Cl^- + I_2}$

Bromine displaces iodide:

$\mathrm{Br_2 + 2I^- \rightarrow 2Br^- + I_2}$

But iodine does not displace bromide or chloride.

Observation: formation of iodine gives brown solution (or purple in organic layer).

6) Iodine as a test reagent (two big ones)

(A) Starch test (iconic)

Iodine forms a deep blue-black complex with starch (specifically amylose helices).
This is used to detect iodine, and also in clock reactions where iodine appears/disappears.

(B) Iodometry / iodimetry (A-Level titration territory)

Iodine can be titrated with thiosulfate:

$\mathrm{I_2 + 2S_2O_3^{2-} \rightarrow 2I^- + S_4O_6^{2-}}$

Starch indicator is added near the end point (when solution is pale) for a sharp finish.

7) A quick word on safety and good lab habits

Iodine vapour is irritant — use a fume cupboard for heating/sublimation demos.
Avoid skin contact (stains and irritates).
Use small quantities: iodine is “spectacular per gram”.

Mini “exam-style” check questions (with answers)

Why are iodine’s melting and boiling points higher than chlorine’s?
Because iodine molecules are larger with more electrons, so London dispersion forces are stronger.
Write the ionic equation for chlorine reacting with potassium iodide solution.

$\mathrm{Cl_2 + 2I^- \rightarrow 2Cl^- + I_2}$

Why does iodine appear purple in cyclohexane but brown in water?
Cyclohexane dissolves molecular I₂ well (purple). In water iodine is poorly soluble and can form I₃⁻ in the presence of I⁻, giving brown shades.
State the half-equation for iodine being reduced.

$\mathrm{I_2 + 2e^- \rightarrow 2I^-}$