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Resources

Below you will find a resource list and a sample question and answer. 

Resource List

Core Engineering Texts

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  1. “The Science of Formula 1 Design” by David Tremayne
     

  2. “Car Science” by Richard Hammond (Great intro for younger readers)
     

  3. “Race Car Vehicle Dynamics – Simplified” (student edition by Milliken)
     

Articles (Free & Readable)

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NASA’s Beginner’s Guide to Aerodynamics (Car Physics)

YouTube Channels & Videos

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  • Engineering Explained
     

  • Donut Media – “Up to Speed” & “Science Garage”
     

  • Driver61 – Race Car Engineering Series

Math & Physics Foundations (Applied to Engineering)

These provide the math and science fundamentals needed to understand car dynamics, performance optimization, and trade-offs.

Books / Resources

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  1. “Physics for the Inquiring Mind” by Eric Rogers - Excellent conceptual grounding in mechanics, friction, motion.
     

  2. CK-12 FlexBooks – High School Engineering, Physics, and Trigonometry - Free, editable textbooks with practice problems.

Videos

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  • Veritasium – Mechanics of motion, energy, real-world applications.
     

  • MinutePhysics – Physics concepts in digestible visual form.

Supplementary Resources (Cross-Disciplinary & Interactive)

Websites & Simulators:

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  • PhET Simulations – Try “Forces & Motion” or “Energy Skate Park”
     

  • GeoFS Flight & Car Simulators – Model performance in changing conditions.
     

  • Algodoo – Playful 2D physics sandbox for testing force, drag, and friction concepts.
     

Videos for Broader Inspiration:
 

  • Making Stuff Faster – PBS NOVA (explores car design, speed science)
     

  • F1: Drive to Survive (Netflix) – While dramatic, it can be paired with technical discussions about aerodynamics and telemetry.

Digital Tools & Simulations

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  • GeoGebra
     

  • Wolfram Alpha
     

  • PhET Interactive Simulations

Sample Engineering Question and Answer

Question

Prompt:


An airline operates a short-haul passenger jet with the following parameters:

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  • Empty weight: 95,000 lb
     

  • Maximum take-off weight: 140,000 lb
     

  • Current range: 900 miles
     

  • Fuel capacity: 6,875 gallons of Jet-A
     

  • Fuel consumption rate: ~0.50 lb/(lbf·h)
     

  • Engine thrust: 28,000 lbf per engine (2 engines)
     

  • Cruise speed: Mach 0.78 (≈515 mph)
     

  • Cruise altitude: 35,000 ft
     

  • Operating cost: $700,000 budget for retrofits
     

Your task is to modify the aircraft to:

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  1. Reduce fuel consumption by 10%
     

  2. Extend the aircraft’s range from 900 to 1,100 miles
     

  3. Stay under 140,000 lb take-off weight
     

  4. Stay within the $700,000 upgrade budget
     

You may change:

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  • Engine (not thrust rating)
     

  • Fuel type
     

  • Aerodynamics
     

  • Fuel tank capacity (add internal tanks only)
     

  • Interior or cargo weight
     

  • Avionics or software
     

Show all calculations and justify your design.

Answer

Energy Requirements

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Current fuel capacity:

  • 6,875 gal × 6.8 lb/gal = 46,750 lb of Jet-A fuel
     

Current total loaded weight:

  • 95,000 lb (empty) + 46,750 lb (fuel) = 141,750 lb (already over MTOW)
     

The aircraft is likely flying under-fueled to stay under the 140,000 lb MTOW. Assuming it carries 45,000 lb fuel max to stay within limits (with 95,000 lb airframe and 0–1000 lb cargo/passengers).
 

Reduce Fuel Consumption by 10%
 

  • Replace older turbofans with CFM LEAP-1B engines
     

  • These provide same 28,000 lbf but ~0.38 lb/(lbf·h) fuel consumption
     

Fuel savings:
 

  • Original burn = 2 engines × 28,000 lbf × 0.50 lb/(lbf·h) = 28,000 lb/hr
     

  • New burn = 2 × 28,000 × 0.38 = 21,280 lb/hr
     

  • Savings = 6,720 lb/hr → ~24% reduction in cruise fuel burn
     

Requirement met (exceeds 10% fuel savings)

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Cost:

Engine core retrofit (compressor/turbine) + software upgrade to improve thermal efficiency costs ≈ $400,000, reducing SFC by ~12%.
Use this as our modification.

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Increase Range
 

Goal: Go from 900 mi ➝ 1,100 mi = 22% increase
 

Fuel consumption = cruise burn × time

Time = distance ÷ speed = 1,100 mi ÷ 515 mph ≈ 2.14 hr
 

New burn rate = 2 × 28,000 × 0.44 (after retrofit) ≈ 24,640 lb/hr
 

Total fuel needed ≈ 24,640 × 2.14 = 52,729 lb
 

But aircraft can only carry ≈ 45,000 lb of fuel and stay under MTOW.

So, we need:
 

  • More fuel capacity
     

  • Less aircraft weight
     

Modify Fuel Capacity and Weight
 

Add internal auxiliary tank:
 

  • Add 700-gallon bladder tank in cargo bay
     

  • Adds ≈ 700 × 6.8 = 4,760 lb of fuel
     

  • Cost ≈ $100,000
     

  • Minor structural mod: stays within fuselage = certified
     

Reduce interior weight:
 

  • Replace 3,000 lb of aluminum with carbon-fiber composites
     

  • Use thinner seat frames, lighter flooring panels
     

  • Cost ≈ $150,000, weight saved ≈ 3,000 lb
     

New max fuel onboard = 45,000 + 4,760 = 49,760 lb
 

Total aircraft weight:
 

  • Airframe: 95,000 lb
     

  • Fuel: 49,760 lb
     

  • Savings: −3,000 lb
    → Net: 141,760 lb → still over MTOW
     

Remove one cargo pallet:

  • Drops 2,000 lb of cargo
    → Final take-off weight = 139,760 lb 
     

Change Fuel Type
 

  • Switch to 50% Sustainable Aviation Fuel (SAF)
     

  • SAF has ~3% more energy per lb → effective fuel mass = 49,760 × 1.03 = 51,253 lb equivalent
     

  • Range increases without more weight
     

  • Cost = neutral (offsets from SAF subsidies)
     

Avionics Upgrade
 

  • Add performance management software
     

  • Helps pilots optimize climb/cruise profile
     

  • Estimated fuel/range benefit: ~1–2%
     

  • Cost ≈ $40,000

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Total budget:

Upgrade

Engine retrofit (thermal core)

Auxiliary fuel tank

Cabin lightweighting

Software and training

Total

Cost

$400,000

$100,000

$150,000

$40,000

$690,000 

Final Justification 

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To meet the twin goals of reducing fuel burn and increasing range while staying under strict budget and weight limits, I focused on integrated changes that improve overall energy efficiency. First, I retrofitted the engines with more efficient internal components and software, reducing specific fuel consumption by over 10%, which alone cuts cruise burn by over 3,000 lb/hour. To tackle the range extension, I added a 700-gallon auxiliary fuel tank and compensated for the weight by replacing cabin materials with carbon-fiber components and removing a cargo pallet. This preserved weight margins while increasing usable fuel to nearly 50,000 lb. I then introduced a 50/50 SAF blend, which slightly increases energy per pound and contributes to a net equivalent fuel load of over 51,000 lb, enough to cover 1,100 miles at cruise. Finally, flight management software helps optimize climb profiles and step cruising, giving a final 1–2% range improvement. Together, these modifications keep the take-off weight at 139,760 lb, stay $10,000 under the $700,000 budget, and successfully deliver a 10–12% fuel saving while extending operational range to meet the goal. Every change is grounded in real-world engineering principles: managing mass, maximizing energy density, and improving efficiency through both hardware and software integration.

Alternative Question and Answer

Question

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A car completes a 10-mile circuit with 120 turns in 6 minutes 30 seconds. It has 800 horsepower, weighs 1500 lbs, and runs on 89-octane gasoline. The track surface is smooth concrete, and turn angles vary between 25° and 75°, offering the car a top speed of 180 mph on the straights and an average speed of 50mph in the corners. The car is raced on a winter day. With a budget of $500,000 what performance-oriented modifications would you propose to reduce lap time to 6 minutes, assuming a fixed engine? Consider aerodynamics, tires, suspension, gearing, and weight distribution. Justify your decisions using engineering principles.​​

Answer

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Initial Deduction

  • Distance=10 miles

  • Current Lap Time = 390 s⇒10 miles in 6.5 min

  • Current Avg Speed =10mi 6.5min × 60 = 92.3 mph

  • Target Avg Speed =10mi 6min×60=100 mph
     

We need a 7.7 mph increase in average speed.
 

Key Constraints and Observations

 

  • 120 turns limits gains from horsepower—focus should be on cornering performance.

 

  • Straight line top speed (180 mph) is already more than sufficient.

 

  • Winter temperatures imply colder tires and reduced grip.

 

  • Engine is fixed; no increase in horsepower.

 

  • No mention of track modification rules—so small modifications may be valid.

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Performance-Oriented Modifications 

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  1. Aerodynamics Upgrade (~$100,000)

    Install adjustable front and rear wings to increase downforce.

    Improve underbody airflow with a flat floor and rear diffuser.

    Downforce increases cornering grip by pushing tires harder into the road (increased normal force Fn ⇒ Ff  =μFn).

    Trade-off: increases drag on straights, but net gain in lap time due to faster cornering.

    Estimated gain: +3 mph average in corners
     

  2.  Tire Upgrade with Winter-Specific Compound (~$50,000 per race set)

    Use soft-compound performance tires that heat up faster in cold conditions

    Optionally, install a tire warming system ($10,000) for consistent grip early in the lap.

    Increases friction coefficient 𝜇, reducing slip and improving acceleration out of turns.

    Estimated gain: +2 mph average in corners, improved launch from slow corner
     

  3. Suspension Tuning and Lightweight Materials (~$100,000)

    Upgrade to active dampers or fully adjustable suspension to maximize tire contact in turns.

    Reduce unsprung mass with carbon fiber suspension components and lighter wheels.

    Results in better handling, less body roll, and improved stability.

    Estimated gain: better stability at high G-loads, +1–2 mph average speed in technical sections
     

  4. Gearing Optimization (~$25,000)

    Adjust gear ratios to match power band to tighter corner exits.

    Shorter gears improve acceleration out of slow turns without changing the engine.

    Estimated gain: +1–2 seconds off lap time
     

  5. Weight Redistribution & Ballast (~$15,000)

    Shift weight distribution slightly rearward (~47/53) to improve traction on corner exit.

    Adjustable ballast can fine-tune grip balance between front and rear tires.
     

  6. Data Collection & Predictive Modeling (~$20,000)

    Use lap telemetry + simulation software to find optimal racing line and braking points.

    Even without changing car hardware, optimized driving behavior can save 1–2 seconds/lap.

 

Further Solutions

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  • Run at a Warmer Time of Day
     

  • Tire grip improves ~10% with temperature.
     

  • Minimal cost, easy implementation.
     

  • Could save 1–2 seconds if weather cooperation allows.
     

Track Alterations 

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  • Resurface bumpy corners or improve camber on sharp turns.
     

  • High cost unless minor.
     

  • Improving traction zones could yield big gains.

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Cumulative Impact Estimate

Upgrade 
Aerodynamics

Tires

Suspension

Gearing

Data Optimization

Total Gain    

Avg Speed Gain

+3 mph

+2 mph
+1.5 mph
N/A

N/A

~6-8mph

Lap Time Saved

~ 10 sec

~ 6 sec

~ 4 sec

~ 2 sec

~ 2 sec

~30 sec

Justification

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To reduce the lap time from 6:30 to 6:00, I focused on improving cornering speed and stability rather than engine power, since the 800 hp engine is fixed and already sufficient for straight-line performance. First, I proposed aerodynamic upgrades like front and rear wings and a flat underbody to increase downforce, improving cornering grip. Second, I recommended softer tires optimized for cold weather, which would offer higher traction during winter races. I also included suspension tuning and lightweight wheels to help the car maintain grip and stability through turns. Gearing adjustments would make acceleration more responsive after corners, and data analytics could refine the racing line and braking points. These combined improvements could raise the car’s average speed enough to achieve a 6-minute lap. I also suggested racing at a warmer time of day or minor track improvements as alternative solutions. This approach uses engineering principles from physics, thermodynamics, and systems optimization to justify each decision within the $500,000 budget.

Anti-Plagiarism Policy

 

Zero Tolerance for Dishonesty

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All quiz responses and essay submissions must reflect your own independent work. Any plagiarism, collaboration without permission, or undisclosed AI-generated content will result in immediate disqualification.

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We use advanced software to verify originality and authorship integrity.

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