From a Poster to the Real Thing

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n 1984, at the ripe age of ten, I was immersed and infatuated by the blitz of mid-eighties sports cars being imported to North America. Like every kid, I had the Hot Wheels, the magazines and the posters. In fact, an entire wall of my bedroom was dedicated to car posters. It started with just any "cool car" - but it quickly became exclusive to Porsches. I specifically remember receiving two posters as birthday gifts, a red Testarossa and a white Countach. Both were soon demoted to a lesser wall and eventually rolled up and ungratefully jammed in a closet - unworthy of my Porsche shrine.

I collected posters of all colours and all models: Targas, Carreras, SCs, RSs, 924s, 944s, 928s... but the center of my attention was the voluptuous 911 Turbo (or, as I'd remind everyone, "not just a 911, it’s a nine thirty"). This car, in my preteen mind, had everything in the right place. It was the perfect balance of what a sports car should be: friendly but mean, subtle but aggressive, both Bruce Wayne and Batman. Even a few years later when I was taken aback by the revolutionary 959 (this exact poster), I remained true to my first crush.

Road&Track January 1986 The January 1986 issue of Road&Track cemented it for me. On the cover was a line-up of four guards red Porsches led by the one-and-only, the almighty, 930. I can't tell you how many times I read that article. Whenever the Turbo was mentioned, I would intentionally slow my reading and savour the words.

Growing up in rural Nova Scotia I didn't get to see too many exotic cars in the flesh. However, every few months the family would pile into the station wagon and take the hour-and-a-half drive to "the city". This excursion always became a bit of a hunting trip for me. I'd scan the hundreds of cars whizzing by, waiting for a glimpse of a Porsche...just hoping to see an allusive 930. On the rare occasion I'd get a glimpse of one and would instantly become fixated. I wouldn't be able to pull my eyes away. My dad would joke, "Don't stare son! Maybe that's all the poor fella can afford."

As I neared the age of sixteen, I had the inevitable and disheartening realization that my first car would not resemble any of my posters. So I did some homework and learned that Volkswagens were a not-too-distant relative of the Porsche. With a non-existent budget, I found myself in a ten-year-old hand-me-down grey 1980 VW Rabbit Diesel... <sigh>.

Now fast forward about twenty years and several Volkswagens later. In the Appalachians of Pennsylvania, on a winding mountain road cut through a stand of old-growth ash trees, I find myself behind the wheel of a black 1984 930. The cool fall air slipping over the car, down through the huge intercooler and getting sucked into the hungry 3.3 litre. Half excited and half frightened by the savage snarl behind me, I glance at the tach, depress the heavy clutch and reach for another gear.

Later that day I traded my hard-earned savings for the keys.

That day... Obviously when a lifelong dream is suddenly staring back at you, there is a certain degree of surrealism. Amidst the euphoric haze, my most overwhelming impression was that is was nothing like what I'd dreamt it would be. But of course how could it live up to the immortal superhero conjured up in my ten-year-old imagination - after all, it was just a car. No power steering, no power brakes, big turbo lag, unwieldy in the rear... Don't get me wrong, it was in no way disappointing. It was what it was - and it was real!

In Atlantic Canada we store our collector cars through the winter months, keeping them from the perils of snow and road salt. Surprisingly in some ways this is kinda nice. Watching the snow melt, the anticipation of that first spring drive becomes so climactic. Yesterday was that day once again. As the seat bolsters hugged my sides, I felt the direct steering, the turbo lag - the smells, sounds and textures were all the same ...I got that same involuntary grin on my face and I relived that first drive all over again.

Specific Gravity and Brix/Plato Conversion

If you are buying a new refractometer for brewing purposes, look for one that includes the SG scale (ideally both SG and Brix/Plato) - then you can skip all this conversion nonsense.

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'm sure a lot of homebrewers face this - you get a new refractometer (which usually measures in degrees Brix or Plato) however almost all homebrewing documentation refers to Specific Gravity (SG). So you go looking for a conversion formula - I mean, how hard could it be? When searching you will find a mix of information: a general "rule of thumb" (see below), a few online calculators (that produce varying results) and a bunch of reference tables - all are workable but the inconsistencies are somewhat disconcerting. I'm the kind of guy that needs to know why things are the way they are, so this blog entry is a summary of what I've found.

Specific Gravity

First some background. Specific gravity, or more correctly, relative density, is the ratio of the density of a liquid to the density of pure water.

SG	= DS : DW
	= DS/DW

Where,

• D_S is the density of the sample liquid,
• D_W is the density of pure water, and
• SG is the specific gravity.

So, of interest to brewers, when there is more sugar dissolved in a liquid, like unfermented wort, that ratio is greater than after fermentation. The most common tool used by homebrewers to measure the relative density of a liquid is a hydrometer (or more properly called a saccharometer).

Temperature Correction

When measuring SG with a hydrometer you should be aware of the temperature of the liquid - especially when dealing with hot wort. Warmer liquid is less dense so the SG will read lower than it would when brought down to room temperature. This is important since hydrometers are calibrated for a specific temperature. The following is a formula for the SG temperature correction for hydrometers calibrated at 15°C (59°F):

SG'

=

SG + 1/1000(-2.627634×10-6Ts3 + 2.057793×10-3Ts2 - 1.32674×10-1Ts + 1.313454)

Where,

• SG is the measured specific gravity
• T_s is the temperature of the sample in degrees Fahrenheit (°F), and
• SG' is the corrected specific gravity for a hydrometer calibrated at 59°F.

And of course:

TF = 9/5TC + 32

⇔

TC = 5/9(TF - 32)

Where,

• T_F is the temperature in degrees Fahrenheit (°F), and
• T_C is the temperature in degrees Celsius (°C).

For example, if we have a 40°C (104°F) sample measuring 1.028 in the hydrometer, the formula above tells us that we need to add 0.0068, resulting in a SG of 1.035 - a significant difference.

But not all hydrometers are calibrated for 15°C. So here is a formula for the SG temperature correction for a given hydrometer calibration:

SG' = SG(	2.32820948×10-9Ts3 + 2.04052596×10-6Ts2 - 1.34722124×10-4Ts + 1.00130346	)
	2.32820948×10-9Tc3 + 2.04052596×10-6Tc2 - 1.34722124×10-4Tc + 1.00130346

Where,

• SG is the measured specific gravity
• T_s is the temperature of the sample in degrees Fahrenheit (°F),
• T_c is the calibration temperature of the hydrometer in degrees Fahrenheit (°F), and
• SG' is the corrected specific gravity.

Brewer's Points

Brewers often use a shorthand unit to describe specific gravity called "brewer's points" or just "points". We drop the 1 and multiple by one thousand (moving the decimal point up three spots). For example, an SG of 1.035 is sometimes referred to as 35 points; e.g. 1.035. So mathematically:

BP	= 1000(SG - 1)

Where,

• SG is the specific gravity, and
• BP is the brewer's points.

Refractometers

So why use a refractometer? First of all, refractometers are great because you only need a few drops of sample liquid which reduces waste and risk of contamination. Also, most refractometers have an Automatic Temperature Compensation (ATC) so no correction needed. However, a refractometer actually measures the index of refraction of the liquid, not the specific gravity. The good news is that the index of refraction of a liquid is directly related to its density (affected by, for example, the amount of sugar in the liquid), which in turn can be used to calculate its specific gravity.

Brix / Plato

The units often used to indicate the amount of sucrose in a liquid are degrees Brix (°Bx) or degrees Plato (°P). There's lots of history as to how these scales were developed and evolved; e.g. the Brix scale is based on the Balling scale (other scales include Baumé and Oechsle). For most purposes, Brix and Plato are interchangeable; e.g. 9.99325°Bx = 9.99359°P. Traditionally brewers use the Plato scale and vintners use the Brix scale. These scales correspond to the percent of sucrose in a pure water solution (by weight). So if we have a 1kg solution that we know contains 90g of sugar (i.e. 910g of water), we would have 9% sugar by weight, that is 9°P, or equivalently 9°Bx.

UPDATE: Most refractometers have been designed for measuring sucrose solutions; unfortunately maltose has a slightly different refractive index (and wort contains some other non-sugar bits that alter the solution's refraction). Every brew is a bit different so one way to estimate the difference is to compare your refractometer with a hydrometer for that particular solution. Typically the refractometer will be somewhere around +2 to +6%. Having to use a hydrometer every time kinda defeats the convenience of a refractometer so most people simply adjust their Brix measurement by 4%.

Bx'  ≈

Bx 100% + 4%

=

Bx 1.04

Where,

• Bx is the measured degrees Brix (°Bx) of a maltose solution measured using a sucrose refractometer, and
• Bx' is the adjusted degrees Brix (°Bx).

Conversion Formulas

The relationship between SG and the Brix/Plato scales is not linear, it's close but not quite. Several formulas can be used to approximate this curve. For the Plato scale, here are three functions, from the least accurate to the most accurate: a linear equation (Rule of thumb), a quadratic (Lincoln) and a third-order polynomial (Cubic).

PRule of thumb =	1000(SG - 1)
	4
=	BP 4

Where,

• SG is the specific gravity,
• BP is the brewer's points, and
• P_{Rule of thumb} is the degrees Plato (°P) calculated using the "Rule of thumb" formula.

PLincoln =	(-205SG + 463)(SG - 1)
=	-205SG2 + 668SG - 463

Where,

• SG is the specific gravity, and
• P_Lincoln is the degrees Plato (°P) calculated using the Lincoln quadratic formula.

PCubic =	135997/1000SG3 - 63034/125SG2 + 11117/50SG - 616217/250
=	135.997SG3 - 630.272SG2 + 1111.14SG - 616.868

Where,

• SG is the specific gravity, and
• P_Cubic is the degrees Plato (°P) calculated using the cubic formula.

UPDATE: Here is yet another conversion formula associated with the Plato scale:

PCubic2 =

190.74SG3 - 800.47SG2 + 1286.4SG - 676.67

Where,

• SG is the specific gravity, and
• P_Cubic2 is the degrees Plato (°P) calculated using another cubic formula.

Here is a conversion formula associated with the Brix scale.

Bx = 2613/10 ( 1 -  1 ) SG

⇔

SG =  1 1 -  Bx 2613/10

Where,

• SG is the specific gravity, and
• Bx is the degrees Brix (°Bx).

Conversion formula comparison As you can see, the Plato "Rule of thumb" formula is the easiest to remember and is within one SG point up to 15°P. However if you are brewing imperials or other high-gravity beers, you are better off using one of the other formulas (which are all pretty close).

This brings us full circle to the reference tables. Rather than take the time to run the formula, a lookup table is quite handy (although it's good to know which formula the table is based on). Here (TODO) is one that I made and keep with my refractometer. I also use a clear sheet protector to save it from any inadvertent mash splash.

Calculators

Here are two calculators that use the formulas described above:

Brix ⇒ Specific Gravity
Brix (using a sucrose refractomer):	°Bx ()
Adjustment (for a maltose solution):	% ()
Specific gravity (SG):	⇔   points

Specific Gravity ⇒ Brix and Plato
Specific gravity (SG):	⇔   points () ()
Hydrometer calibration (Tc):	°C   ⇔   °F () ()
Temperature of sample (Ts):	°C   ⇔   °F () ()
Correction (ΔSG):
Corrected specific gravity (SG'):	⇔   points
Plato:	°P(Rule of thumb)
	°P(Lincoln)
	°P(Cubic)
Brix:	°Bx

Audio - Speaker Spades

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few weeks ago I made a blog entry about the construction of some balanced interconnects for my home audio system. At the same time I put together some speaker wires.

The speaker wires are made from similar materials as the balanced interconnects.

Wire materials:

• 16AWG dead soft .9999 silver wire
• Teflon insulation for 16AWG wire
• ¹/₄" O.D. (outside diameter) sleeving
• WBT solder
• Heat shrink

Since my system is bi-amped, I have four pairs (eight conductors) of speaker wires, each 2m in length. The wires have a banana plug for the speakers (Magnepan IIB) and a spade for the amps (Bryston 4B SST). I was able to pick up some cheap rhodium-plated, expanding banana plugs, but I wasn’t happy with the spades on the market, in particular their prices. For the price of eight gold-plated spades, I could easily purchase the materials to make my own solid silver spades. Given the choice, and my unrelenting propensity to Do-It-mYself, I decided to manufacture my own speaker spades.

Dimensions Spade materials:

• 1" x 6" of 12AWG (2mm) sterling (925) silver

Tools:

• Vernier caliper
• Hacksaw, vice
• Files, sandpaper, Dremel rotary tool
• Drill press, drill bits, center punch

Blanks and finished spades This being the first time I’ve played around with a chunk of silver, I first practiced on a piece of less costly aluminum. The malleability was significantly different but I was able to work out sizing issues on the rough prototype.

The Bryston 4B SST Owner's Manual^[PDF] specifies the ideal size of a spade for its binding posts. The 1" x 6" 12AWG sheet was the perfect size for eight 1" x ⁵/₈" blanks with only a sliver of silver remaining after the saw cuts. Each blank had two holes drilled, four more short cuts, and some careful bending, filing and finishing.

Combined with the hydrogen sulfide (H₂S) floating around in the air, silver (Ag₂) turns into silver sulphide (Ag₂S), also known as tarnish.

H₂S + Ag₂(s) → Ag₂(II)S + H₂

Soldered connection and
finished product Tarnished silver does not conduct electricity as nicely as pure silver. It is important to clean and prevent the tarnishing of silver contacts. I used some CAIG DeoxIT^® D5 to clean the surfaces of the spades. DeoxIT is supposed to cleanup oxidation – but silver tarnish is a sulfide... so I’m not sure if it’s the right stuff to use but it seems to work. CAIG marketing materials says it’ll work...

I am quite pleased with the fit and finish of the final product. I won’t claim that there is an audible difference, but it does look pretty cool ...and so does my shop floor with about ten dollars worth of sparkly silver bits.

Automotive – Porsche Speedometer Replacement

The 930 doing what it does best

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urprisingly, having a low-miles, all-original 1984 Porsche 930 can be a real bummer. It’s a ridiculously fun car to drive, and even washing it can be a sensual experience. The problem is that I never get to work on it. Nothing goes wrong (which, actually, is great) and making “upgrades” to such an OEM car is criminal. However, as a habitual tinkerer, having such a fine example of German engineering in my driveway is a huge temptation. This is why I’ve decided to gut it and convert it into a competitive drift car – – joking.

Luckily I’ve been able to satisfy my DIY urges on my VW Super Beetle (and it needs it!). Having said that, I still jump at the opportunity to do work, even if very mundane work, on its more mature, but “übermensch" sibling, the 930. The latest thing I’ve done is replace the speedo (not to be confused with the like-named, tight-fitting, TMI swimwear).

You can find a lot of Porsche 911 Turbos on eBay with questionable odometers (if you plan to buy one, I highly recommend first investing in an AutoCheck account). However, in this case what I’ve done is actually replace the speedometer with the original factory speedometer – a restoration if you will.

When the car was new, it was imported into the United States as a “gray market” car since Porsche was not exporting the 930 model to the US from 1980-1986. As a “Euro” car, it was converted to American standards, which including de-metric-izing the speedo/odometer. The gentleman who did the import and conversion, the original owner who I bought from, was thoughtful enough to keep the original German equipment, and I thank him for that. I live in Canada and I benefit from the superior metric system, thus my motive to do the swap back.

The American miles odometer has about 20,000miles (about 32,200km). At the time of putting it back in, the original had only about 340km.

Backside

The replacement is easy with only a few considerations – primarily where to hookup each wire. The instrument pulls out without any tools (but a good amount of fingertip strength is required and maybe a push from the back). Once out, grab your toolbox camera and take a snapshot of the existing wire hookup. Compared to the metric instrument, the terminals in the same locations can be used.

Before and after

The internals of the instrument are clever enough to accommodate the differences in scale as well as different upper range of 300^km/_h (186mph) instead of 150mph (241^km/_h). And yes, its documented top speed is 278^km/_h (173mph) – fourth gear at 6750RPM...and remember, this is a stock production car in 1984! And no, I have never driven that fast.

Now don’t worry, I plan to keep the “miles” speedometer with the car as part of its history – and not pass the car off as a 400km car. That said, I am curious how my local Registry of Motor Vehicles will handle the swap – have I just done something illegal? I’ll follow up next year when I get my next Motor Vehicle Inspection.

Audio - Balanced Interconnects

Installed

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n an earlier blog entry I described my bi-amping adventures. A key part of getting the whole setup put together was building balanced interconnects. I made two 10m runs of Belden 89207 to connect the pre-amp (at the back of the room) to the crossover (up front) and four ¹/₂m silver interconnects to link the crossover to the amps.

Since the Belden cables aren't very interesting, I'm going to focus this blog entry on the silver ones. The materials I used are:

• 24AWG dead soft .9999 silver wire
• Teflon insulation for 24AWG wire
• Three-pin XLR3 connectors
• ¹/₄" O.D. (outside diameter) sleeving
• WBT solder
• Heat shrink

As an aside, Rane provides all kinds of other great audio documentation in their RaneNotes.
(or open directory).

Most balanced cables use XLR connectors. The ones I made are no exception. When making any audio cable, Rane provides a great document on Sound System Interconnection^[PDF].

There are a lot of exhaustive explainations on the Internet about how balanced cabling works. But the Coles-Notes of it is: a balanced cable, or more correctly, a balanced system, works to eliminate any noise being introduced along the length of the cable.

XLR3 connector

To achieve this, it all starts at the source device. Three conductors are used:

	Pin 1	Ground
	Pin 2	Hot +	Carries the signal
	Pin 3	Cold -	Carries an exact copy of the signal, but inverted phase

Ground - Hot - Cold

Now consider if some kind of noise is introduced along the wire. For the most part, the noise will affect the Hot and Cold in the same way.

Once at its destination (the load), effectively the Cold can be re-inverted to the same phase as the Hot. Notice, by doing this, we’ve also inverted the noise that was introduced to the Cold signal. This inverted noise, coupled with the noise on the Hot will cancel, leaving you with the combined original signal. Clever, eh?

So technically, the "balanced" part of a balanced cable has more to do with the source and load devices than the actual cable. However there are a few features of the wire itself which helps reduce the chances of noise being introduced. The twisting of the two signal wires help reduce interference from electromagnetic induction. The ground, usually a shielding mesh which surrounds the twisted pair, provides a dedicated ground, not part of the signal like an unbalanced cable, and prevents possible ground loops.

When making such short interconnects (in my case from the crossover to the amps), the benefits gained with balanced cables is likely very little. Since there is more opportunity for external noise to be added to the signal in a longer length, my 10m interconnects from the pre-amp to the crossover are a more typical use of balanced cables. However, even with a very short cable there is still a chance of external noise, especially in an unfriendly environment. Also, regardless of length, the XLR connector provides a good, secure locking connection.

Teflon (polytetrafluoroethylene, a.k.a. PTFE) is often used as a wire insulator because it's such a good dielectric (it has a resistivity of 10²² to 10²⁴ Ω·m – that’s about 10,000,000,000 times that of glass! ...more about resistivity below). Its slippery nature and high heat resistance is great for making omelets, however, in this case, these properties aren’t of much interest.

I decided to simply braid the three wires. There are a lot of articles and theories about the optimal relative placement of the three conductors. I’ve read too many different and opposing opinions – so I decided to start simple with an ordinary braid and make my own judgment as to its performance.

Finished cables

For sleeving, I put the braided trio in a semi-transparent ¹/₄" sleeve - actually the sleeve is plastic tubing typically used as the waterline to the ice maker in your refrigerator. There are a ton of other cheap sleeving options including using shoelaces or no sleeving at all. Some folks will claim there are acoustic properties to different insulators and sleeves – maybe - but my considerations were primarily protection and secondarily aesthetics.

So why use silver wire instead of copper? The long and short of it is that silver conducts electricity better than copper. How much better? Well only an audiophile is unbalanced enough to justify the cost-benefit (yah, I know, bad joke).

Conductivity, actually on the flip-side it's called resistivity, is measured in ohm meters (Ω·m). The resistivity of silver (Ag) is 15.87nΩ·m (at 20°C). The resistivity of copper (Cu) is a poky 16.78nΩ·m (again, at 20°C).

So consider:

ρ = R

A ℓ

Where:
  ρ is the resistivity in Ω·m
  R is the resistance in Ω
  A is the area of a cross-section in m²
  ℓ is the length in m

A 24AWG wire has a cross-section area of 0.205mm² or 2.05x10^-7m². Divide this by a length of 0.5m. Now solve for R when ρ is 1.587x10^-8Ω·m.

1.587x10-8Ω·m = R

2.05x10-7m2 0.5m

R = 0.0387Ω

So for an equivalent copper wire, ρ is 1.678x10^-8Ω·m.

R = 0.0409Ω

...a difference of a whopping 0.0022Ω! Okay, so not a huge difference but it is a 5.4% improvement over copper. So you've got two options: use slightly heavier gauge copper, or spend way more, use silver, swear you can hear the difference and do the math to try to prove it.