Water Condensation & Fuel Tanks

How much liquid water is generated in a fuel tank due to condensation? This is an engineering analysis focused on aviation, where water in the fuel tanks is a known cause of accidents. There is plenty of anecdotal evidence and opinions ranging from “Never happens” to “Critical in humid areas”. At the end of this note, you will be able to understand the physics and quantify the generation rate. Let’s get started.

Summary

  1. Nearly empty light-aircraft tanks in extreme hot and humid environments with extreme temperature swings theoretically could condense approximately a couple of fluid ounces a week.
  2. The generation rate linearly scales with empty tank volume and humidity, but exponentially with temperature.
  3. Normally vented tanks substantially reduce the water influx rate, but do have a breathing mode that can pump moist air during temperature and pressure swings.
  4. Condensation is more likely to be a long term storage threat; Large volumes of water are more likely to be ingress of liquid water.

Dry & Wet Air

Water is a key enabler of life and dramatically affects the behavior of air. We call “dry air” the mixture of mostly nitrogen (80%), oxygen (20%), and trace other constituents (Ar, carbon dioxide, etc). “Wet air” is what we normally encounter and is dry air + water. “Air” could also include particles + bugs + dirt. You can learn more at my course notes here for an introduction and here for non-standard atmospheres.

The important takeaways are:

  • Adding water decreases air density since water has a lower molecular mass than air. (Technical note: Water has 2 Hydrogen of mass 1 plus 1 Oxygen of mass 16 for a total of 18. Air on the other hand has 80% diatomic Nitrogen of mass 28 and 20% diatomic Oxygen at mass 32 for a total of 28.97.).
  • Increasing temperature substantially increases the absolute water carrying capacity of air. Water vapor at 100% relative humidity consists of 0.7% of the wet air mass at 50 F and 6% at 110 F, but a whopping 15% at 140 F. This is why pilots need to be much more concerned with high humidity at high temperatures and not so much at lower temperatures (This is in addition to the temperature effects on density altitude).
Figure 1: Water Carrying Capacity of Air & Figure 2: Saturation Pressure of Water Vapor

The saturation pressure (Ps) in Figure 2 is generated from the Arden-Buck approximation as an exponential function of temperature. This also indicates the pressure at which boiling occurs (e.g. 212 F at sea level pressures of 14.69 psi; and 200 F at 10000 ft with a pressure of approximately 10 psi).

Design a worst case scenario

Let’s pick a scenario where a nearly empty 25 gallon tank completely condenses the water vapor. Plus there is a complete air exchange/recharge of hot and humid (120 F and 100% relative humidity) air once per day. How much water is generated?

The answer is about 0.25 oz (7.5 ml) per day. Consider it one cupped-hand of water, or about a 2.5″ spot of water, or 0.75 seconds of fuel at 10 gal/hr. That’s enough to fully grab your attention.

The rate scales linearly with the tank’s air volume so keeping the tank 90% full reduces the generation rate by 90%. Being in 30% humidity air reduces the rate by 70%. Doubling the elapsed days doubles the generated volume. Notice that the rate exponentially scales with temperature (ps/T is exponential).

Critically, we can bound the generation rate. For example, at 120F and 100% humidity with a 20 gallon tank, the rate should be less than 0.20 oz per day.

If you are generating more than this, chances are extremely likely that there is another mechanism responsible. Go find it.

Maximum Condensing Case with an more Realistically Vented Tank

To be continued

Cold Soak & Descent

To be continued

Decibel (dB) Simplification.

Or… How I learned to stop worrying and count the zeros

The dB decibel scale can often be very intimidating to others, so here’s a quick way to simplify (i.e. no logs or powers) your explanation to two steps. The fundamental point to make is that a Bell is how many zeros. A decibel is the number of zeros multiplied by 10.

Let’s convert a ratio to dB. Pick 100. This number has a number 1 followed by two zeros before the decimal point.

  • How many zeros? “2”. Multiply by 10. “20”
  • Say that number. “20 dB”

Let’s reverse the process and convert dB to a ratio. Pick 40 dB.

  1. Divide by 10. “4”
  2. Four zeros before the decimal place is: “10000… ten thousand”

How about a more complicated case. Convert 25 dB to a ratio.

  • Divide by 10. “2.5”
  • Two and a half zeros before the decimal place is? “more than 100 and less than 1000” Yes, and half a decimal place is about 3. “So 300?” You got it. “25 dB is about 300”

Now, convert 564 to dB.

  • How many zeros? “Almost the number 6 followed by two zeros. So 2” Yes, but we had a 6 in front of the zeros. 6 is worth about 75% of a decimal place. “So 2.75?” Exactly, now multiply by 10. “27.5”
  • Say that number. “27.5 dB”

This approach is much easier to explain than defining dB = 10 log(R) and the inverse operation using pow(10) and gives much better intuition. So, in field work, I tend to just use this approach. This may seem trivial to experts, but any trick to increasing understanding and explain-ability is worth your consideration.

Robust Communications:

Q: How can I improve my communications?

A: This is an excellent question. In this note, you will learn some fundamentals and tools of effective and robust communications.

Part 1: Speaking

First, listen to this lecture.

A brief aside: My experience as a professor taught me that its easy to talk about what I just spent hours preparing. In fact, 4 years of teaching made me FAR better at engineering than 4 years of engineering school. Why is that? I really believe the difference is engagement. I had to be ready to engage a conversation spontaneously. This meant that I had to know and understand.

If in the future I teach another class, I would have students make their own set of formal notes and example problems with solutions. No traditional homework.

Part II: Writing

There is a spectrum of communication effectiveness. Listen to this lecture.

Send me your comments. I look forward to hearing from you at oneill@aerofluids.com

Piper PA-28 Cherokee Wing Comparison: An Aerospace Engineering Perspective

The Piper Cherokee constant chord “Hershey Bar” and tapered wings exhibit significantly different landing behaviors. In particular, the newer tapered Cherokee wings are known -two examples are at https://www.flyingmag.com/rectangular-wings/ and at pilotfriend.com– to give substantially longer landing float than the constant chord wings -all other things being equal. In this note, I will discuss 4 reasons for this behavior and allow you insight into how design choices affect performance.

A Starting Point: Geometry

For the purposes of this engineering note, we will focus on the 180 hp versions: the PA-28 180 (constant), PA-28 180 Extended and PA-28 181 (tapered). The geometries taken from three POHs are in Figure 1:

Figure 1: Piper Cherokee Wings: PA-28 180 Constant chord (left), extended (center) and PA-28 181 Tapered (right)

The aircraft are essentially identical except for the wing planform, so for more insight, zoom into the wing shapes with Figure 2.

Continue reading

Mystery Hs-126 Photo

The following Henschel Hs-126 is from our family’s photo archive. This photo was attributed to my grandmother’s brother W.E. “Bud” Hills of the 101st Airborne in WW2. We suspected the photo was taken in France or Germany. There are no annotations.

Henschel 126; Hs 126; WW2

The aircraft is a Henschel Hs 126, an observation aircraft developed in the late 1930s and essentially obsolete and out of production by the early 1940s. The Hs 126 is a surprisingly large platform given the mission. One successor, the amazing Fiesler 156 Storch outperforms the Hs 126 for short, rough, and unprepared flight operations. The other successor, the Fw 189 “Flying Eye” was superior for observation. The aircraft type was rarely used on the Western front after 1940, most were sent to the Eastern Front.

The markings are 5F+GH. Using public sources of German squadrons and locations, we discovered that this aircraft (“G”) was assigned to the 14th Reconnaissance wing (Aufkl. Gr. 14) 1st Staffel (“H”). This would be 1.(H)/14 with known locations in France from 1940 to 1941. The unit was sent to the Eastern front in Feb 1941 and disbanded while back in France in 1942. The Short Range Reconnaissance wing (Naraufkl. Gr. 14) was created in 1943 but was stationed outside of France. Any use of Hs 126 aircraft in 1944 would be unlikely as Me-109Gs were assigned to the unit. Operationally, the Hs 126 was not feasible in 1944.

This leads to the strong possibility that the photo was taken in 1940 during or after the Battle of France. Thus, the photo was brought back by my relative and not taken by my relative. There are other possibilities, but this is the most likely.

Question: What is the make, model and year of the car in the background? Where is the house style/architecture usually seen? Send comments to oneill@aerofluids.com

Power Induced Dihedral

I recently received a question about the effects of propeller thrust on aircraft stability and control (S&C). Within the aircraft design community, we know that power effects to S&C can be a significant engineering effort. Often, the quantification of these effects requires a powered wind tunnel test with a commensurate pricetag. With in the pilot community, we know that power -and especially propwash- significantly impacts (pun intended) the tail’s aerodynamic control power. There are jet aircraft (ex. YC-14, AV-8) using jet exhaust to provide lift and other reactions.

One interesting historical case of a power induced dihedral is the Martin 2-0-2 prototype from the late 1940s. First, let’s discuss the theory. For a twin engine propeller aircraft, the natural design configuration is mounting the engines on nacelles mid-span and in front of the wing.

We also know that the propwash has a higher dynamic pressure resulting from the increased flow velocity. The propwash during a sideslip is thus non-symmetric across the wing panels (i.e. more outboard on the downwind panel and more inboard on the upwind panel). The asymmetric flow pattern will induce a roll moment into the sideslip. We call this an anhedral effect (i.e. a positive C_L_beta), which is usually detrimental to the aircraft’s flight dynamics.

In the Martin 2-0-2 design, the prototype encountered S&C problems during flight tests. The solution was to considerably increase dihedral in the outer wing panels. This wing joint would later become a fatigue problem (https://aviation-safety.net/database/record.php?id=19480829-0&lang=en) corrected with the 2-0-2A. Overall the aircraft was not known as a success.

Martin 2-0-2 Production Aircraft
By Bill Larkins – Martin 2-0-2, CC BY-SA 2.0

A derivation of power induced dihedral is shown below. Notice that the magnitude depends on the angle of attack; the effect is worst at low speeds with high power settings.

Feeding your Wolf

There is an old story from an unknown Native American tribe. A wise grandfather tells his grandson that there are two wolves battling inside him. One good and one bad. The grandson asks,

"Grandfather, which wolf wins?". 

The careful reply is,

"The wolf I feed."

Which wolf are you feeding?

This note is written in the time of the Corona virus (2020). You are probably at home. You may even be newly graduated engineering PhD or BS but without a job. Right?

Wrong, you already have a full-time job: You. Your full time job should start to later than 8:00am and end no later than 6:00pm every workday. Give yourself Sunday to rest; you will need it.

Your job search is a priority. Somebody is hiring; you just don’t known them. They don’t know you. You have a unique opportunity to impress. Make a list of engineering skills that you can learn, improve, or teach. Start with these:

  • Learn how to use CATIA. Get a student license for $100. This is an essential communications skill.
  • Start a website detailing your skills and capabilities
  • Teach a short course and post on Youtube. Break into 15 minute segments and use a screen capturing program to show the process.
  • Learn how to use rendering software. This skill allows you to make compelling proposal and project graphics.
  • Volunteer to be a journal reviewer
  • Learn how to simulate electrical systems with LTspice
  • Learn how to simulate structural or fluid systems. Example ANSYS.
  • Learn how to use Simulink in Matlab
  • Join an association outside of your area of expertise. Do a deep-dive into the association’s library of materials. Take notes.
  • Get your Part 107 unmanned pilots license. Get your Technician or General class amateur radio license. Find other certifications that you can complete.
  • Update your python programming skills. Make a GUI multi-threaded frontend for a task that you use often. Post on website.
  • Practice writing.
  • Take an AI/ML course: OCW or youtube or a book.
  • Read through all of the SBIR projects offered by NASA, DoD, DOE, etc. How do your skills match? Find and document a project that you could feasibly complete. Search through old SBIR funded announcements and see which company won similar projects. Send your project capabilities to this company. Voila; instant job opening.
  • Get a post-doc position.

Make a deadline. Complete on-time. Show deliverables.

Why does this work?

Pareto’s 80/20 rule: https://en.wikipedia.org/wiki/Pareto_principle

  • 80% of your colleagues won’t search for ways to improve.
  • Of those remaining, 80% won’t finish & document even one task.
  • The 4% (i.e. 20% ∙ 20%) are exactly what your future boss is searching for in a new employee. You demonstrate competency and are low-risk.

I believe that you should update your resume with a “Quarantine” work history showing what you accomplished. The key point for your future boss is demonstrating a strong work ethic at-home with no supervision. This requires documentation and links to delivered product/projects.

Now, go feed your wolf.

Continue reading

Flight Test Engineering Course (UA)

In the Fall of 2019, I developed and taught a course in Flight Test Engineering to a select group of undergraduates in Aerospace Engineering and Physics.

Topics were divided into 1) performance, 2) stability & control, and 3) logistics, operations & hardware.

  • Performance
    • Atmosphere
    • Airspeed
    • Airspeed & Static Port calibration
    • Takeoff
    • Stall
    • Climb Theory
    • Sawtooth climbs
    • Level acceleration & Excess power
    • Level Flight Performance
  • S&C
    • S&C Theory
    • Neutral Point Estimation
    • Stick Forces, Stick force per g
    • Maneuvering Point
    • 6 DOF Aircraft Dynamics
      • Phugoid
      • Short period
      • Spiral
      • Roll substidence
      • Dutch roll
    • Flying & Handling Qualities
    • Inertial Coupling
  • Logistics, operations, & hardware
    • Data reduction
    • Flight test instrumentation
    • Telemetry
    • System identification

Lecture note samples:

The students were required to learn the theory, maneuvers, and analysis necessary to conduct flight testing. We used experimental data collected by the instructor (me) and the students.

Textbook: I assigned Kimberlin’s Flight Testing of Fixed Wing Aircraft; however, Ward’s Introduction to Flight Test Engineering was a primary resource.

Wing Vortex Question

Q: Could you explain to me why the vortex does not appear to be coming from the tip of the wing, but rather several feet closer to the fuselage on this Boeing 777?

Boeing 777 vortex – Unknown photographer

A: Good question. The answer is that the vortex is visible where the change in lift distribution -and thus, shed vorticity- is highest. The flaps are extended, which creates a sharp discontinuity in the wing geometry and lift distribution.

Here’s the physics:

  1. The extended flaps increase both the wing area and the effective angle of attack for the inboard wing. (see: Thin airfoil theory)
  2. The increased area and angle of attack increase the lift being generated on the inboard panel.
  3. Shed vorticity is proportional to the spanwise derivative of the lift distribution.
  4. The vortex rotation decreases the local air pressure and temperature below the dew point. Water vapor condenses into a fine mist. We see this fine mist.
  5. The vorticity is transported downstream (i.e. Helmholtz rule #3)

More information:

  • Notice the spanwise lift coefficient is visually displayed with a vapor cloud above the upper wing. This cloud confirms that the spanwise lift coefficient has the largest decrease at the flap tips.
  • You should remember that the entire wing is shedding vorticity. We see the vortex at the flap tip. If the humidity were higher, we might see additional vorticies.
  • Ground effect is responsible for the slight outboard track of the visible vortex. As the aircraft descends further, the shed vortex will likely be pushed further outboard; induced drag (for a given CL) will decrease.
  • It is not true that a vortex is only generated at wingtips or flap tips. Physics demands a smooth lift distribution (regardless of what we see).