how to program a TI 89 (calculator) for navigation

Something practical to avoid spending too much time with calculations for navigation, especially when the sea is rough and when we have a heavy meal inside our stomach, ready to leave it, probably on the map to draw a new iland, or in the companion way : if we program a calculator before, we get more time instead of waste it inside the boat, it's less boring and the most of time we avoid some seasick problems.

on internet "l'almanach du marin breton" has published programs ready to be included in a TI83 calculator for the height line, the sun's height range, and capable arcs. For a TI89 those programs work very well, there are just one or two small things to do:

On the file, "E" symbol is not the exponential fonction. it's a kind of scientific abreviation : E^2=100, E^3=1000…And when we use it we don't write the "^"on the calculator's screen. In a program we always have to indicate every time the program's end “IF” by a “ENDIF” otherwise the calculator will score “syntax error” something like that. that's why on the line 2 of paragraph “celestial mechanics in the Julian calendar” the sentence does not end with “End” but “Endif”. in the program useful to get the sun's height range we have to add up “Endif” Missing for the program validity.

when we are looking about those programs, we are able to guess others like a meridian program, the orthodromic distance, orthodromic's angle, or a program able to give our distance from a seamark with a known height:

0001 (Copier)

0002 (Copier)

For the calculation of the solar declination, marin breton's program take care of the elliptic nature of earth motion around the sun (part: “celestial mechanics in the Julian calendar”) which gets involved in declination's evolution all the year, and begins from an accurate sun's point in the time. Nevertheless there is a simplified formula to get sun's declination which doesn't care about the elliptic shape of earth's motion but coniders it like a circle (in our reality it's almost a circle, its elliptic shape is very weak with an elliptic excentricity roughly equal to 0.017. a circle's excentricity is 0 to have a little idea). This formula, less accurate than the first one displayed at the beginning, is still efficient even useful and in the same time very simple!

Déclinaison=(23+26/60)*sin((360/365.256363)*(284+J))

This formula is a precious tool to make a little sun's declination program depending on the day, the month, the hour (for 2015 when we compare it with marin breton's program difference is not overtaking 1 degree around mid-October, for the rest it's pretty accurate) without having ephemeridis on board. A second program allows us to have a better result (because we consider the elliptic shape in that way) :

0001 (Copier)

0002 (Copier)

0003 (Copier)

For those declination's formulas we use a sinus fonction because if we write year days and declination's values ina same coordonate system, we get a sinus shape. with a cosinus fonction instead it would be possible. for sinus fonction parameters, in fact how to cope with it to change its period, its range and its departure point it's quite simple : we will use this exemple : A*sin(B(x-H)). "A" parameter adjusts the range's fonction (maxi and mini value it can reach), "B" adjusts period because sinus fonction's period is equal to 360/B ( absolute value). "H" parameter adjusts the phase, For exemple the fonction y=sin x is an impair fonction with a symetry center which is o origin, so if x=0 then y=0. if now we have y=sin (x-3), then y=0 if x=3 so we will have shifted sinus fonction about 3 on the right on absciss line, we have phased it about 3 finally.

 

Solar panels

This is a panel of several solar cells(about forty)connected in series. a solar cell is made of two silicium's plates, in each plate was added small amounts of elictricity drivers like bore inside the positive plate and phosphore into the negative plate. light will disrupt balance towards the plates and bring electrons motions, thus electricity.

1)Light

Also called electromagnetic wave(in star trek or something else, c’est pas sorcier ou question pour un champion), this is the only one wave able to move beyond the void(unlike sonic waves, for instance. When a ship in star wars is farting in a big badaboum it's not possible). Its speed in a vacuum is almost 300000 km/h, and nothing known can exceed this speed. the more light will meet a dense thing, the more it will be slew down and deviated(on the other side we have the sound's speed which is always growing with density). One can consider both the light as a wave and a plurality of particles, photons. a photon is heaviless and neutral, that's why it can move until the highest speeds. a photon's energy increases with light's frequency. for exemple a photon's gamma ray brings really billions of time more energy than a photon's radio ray. gamma, radio, mojito….what does it mean ?

Just as light(visible) is only a part of the electromagnetic waves range. Their spectrum covers a lot of several kinds of waves, from long wavelengthes(several km)to small wavelengths(smaller than an atom size). Electromagnetic waves include: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays finally with the shortest wavelengths, therefore the higher frequencies. in fact light could be seen as an energy's motion "quantified" from little photon's packs to little photon's packs.

the two light sides wave/particles have been discovered because of the photo electric effect, light that strikes metal drives it to send electrons. we have noticed that a weak blue light could move those electrons , but not a strong red light. Why ? because a photon “blue light” will have a higher frequency than “red photon”, so he will be able to dislodge the electron unlike the red one. when an atom's electron touches a defined energy level it jumps on a higher orbital or it isn't, no way it keeps quiet. And when it touches this energy level and there is no higher orbital from where it was laying on the couch watching TV, well he moves his ass…thus if there is electron butts motions, there will be electricity!

Summary, the less light will be filtered by atmospher, the more it will keep energy, its high frequencies able to activate electron motions into the sun cell, therefore induce current! that's why a sun panel will be more efficient with a clear sky and a high sun .

2)Panel

Small diagram of a photovoltaic cell:

photoelectric cell

The negative side(N) is doped with atoms having more electrons than silicon(here, phosphorus), and the positive side is doped with atoms having less electrons than silicium(the positive face P, here bore). When photons will strike the N face, if they carry enough energy they will initiate electron's transfert towards P face, creating electric juice. the power given by the sun on the earth floor is around 1 kw/m2, but the yield of cells generally does not exceed the 20% Thus for a panel 1 m2 not more than 200 watts roughly.

3)several kinds of panels

There are basically three types of solar panels:

.the monocrystalline, it has the best yield. It is blue uniform but it is expensive on the other side.

.the polycrystalline, with a yield slightly worse, cheaper too. It is and blue marbled.

.L’amorphous, weak yield but steady whatever the light strength available. Cheap, uniform color brown / gray.

crystalline cell

Notice: the panel shall be as possible in face with the sun, inclination must consider the latitude of the place, thus the panel should be on a swivel support.

Notice: panel's performance will become null if 50% its surface is masked.

Notice: never clean the panels with chemicals. Clean water regularly to maintain good performances.

Notice: even with the maintenance time after time the yield will decrease.

4)Connections

Generally behind the sun panels there is a box which includes by pass diodes, it's useful to avoid a battery unload in panels. If there is no by pass diodes it should be set up. if we fix several panels with a load distributor we could forget those diodes. To avoid overloading a regulator or a load limiter should be installed too, as for wind turbines.

Two panels in series doubles their voltage produced, connected in parallel it doubles their power(ampérage)produced. we need to separate panels with by pass diodes. It is obviously necessary to adapt the diameter of the cables connected by the current strength and the distance between the panels and the battery. Ouàlaouala en gros quoi.

 

Resins

For polyester boats, there is a choice of resins with different properties. This choice will depend on the fiber fabrics used, the method of manufacture or repair , desired characteristics and of course the price. The main characteristics of these resins are UV resistance, moisture resistance, elevated temperature resistance, shrinkage(volume loss on drying), thixotropy(viscosity of the resin).

1)The polyester resin

This is the most common because of its large range of use and its price. This liquid resin solidifies(polymérize)by the addition of a catalyst(organic peroxide, generally PMEC), and the start of the reaction work with an accelerator, cobalt. The accelerator is used to control the polymerization time, and catalyst function is more made to balance drying time on ambient temperature. Anyway now, for safety reasons almost all resins are pre-accelerated, cobalt is already mixed inside and the last thing to do is to add up the catalyst(add between 1 and 3% of catalyst into the resin, the more cold and damp conditions are, the more we will be close to 3% of catalyst. the average quantity is 2%). Never put too much catalyst otherwise the resin will not dry and polymerize normally(crackles, mixture of resin will heat and the bottle will melt), it will not solidify if catalyst quantity is not enough.

There are two kinds of polyester resins, isophthalic and orthophtalic resins; orthophtalic is the cheapest, but less waterproof(significant water absorption)and therefore more vulnerable to osmosis(slow and progressive infiltration of water into the polyester hull). In addition their mechanical properties are also lower. In fact for nautical things we use the iso resin(better impregnation of fabrics, better resistance to water and chemical products, so in one word it' s better!).

The polyester resins can be loaded(silica, fiber microballoons…)to increase their thixotropic skills to make filler or plaster for filling holes for exemple. It is used to impregnate glass fabrics, kevlar, but not with carbon fabrics. During fabrics impregnation, you have always to alternate a layer of roving(weft fabrics)with a mat layer(fabrics with bulk fiber). For a good finish it is best to always begin and end with a layer of mat(easier to sand), a mat layer impregnation expects two resin doses of a roving mat soaking.

The main problem with iso resin is water absorption, indeed their moisture uptake may be important, causing a decrease in mechanical properties which can lead to delamination(layers division, yeah…). To protect iso resin from water it must be isolated, with a gel coat or polyurethane paint(two-component)like a skin.

Summary: when you use iso resin, always protect the fiber with gel-coat or two-component paint, alternate mat/roving layers, polymerize with catalyst(PMEC)no more than 3%, poor adhesion on wood, use for fiberglass, Kevlar fabrics but not on carbon.

2)Epoxy resin

More expensive, but a lot of benefits. Its water absorption is very low, it has better mechanical qualities, more resistant in face with time and delamination. We also get a better weight / volume ratio, significant for racing boats for example. this kind of resin is rot-proof, it sticks on almost everything(like wood). this is the best resin! However against UV its resistance is weak. Epoxy layers provides better thermal insulation also.

To dry this time we use a hardener(generally a volume of hardener for two volumes of resin, anyway this is indicated on the box), However volumetric ration between hardener/resin must be very accurate and temperature must provide the best drying conditions, otherwise it's failing. This resin may also be loaded with silica(to control the viscosity of the resin, increase the density of the mixture), microfibers(wood sticking) or micro-balloon(Low density plaster, reinforcements in the soul to pass a bolt or run a reinforcement).

When the fabric is impregnated with epoxy resin, mat fabrics is uneeded. It can be used for carbon fabrics. The low shrinkage of this resin allows the use of fewer amounts too.

To protect the epoxy layers from UV polyurethane paint is applied over, the gel coat does not suit. In fact there is a sentence to remember for epoxy: “Epoxy sticks on everything but nothing holds on epoxy( except the two-component paints, and epoxy)”.

Summary: very water-proof, excellent mechanical properties, little shrinkage, weak against UV, expecting more things(dosage resin/hardener, temperature, humidity), used to laminate wood or impregnate carbon, mat fabrics uneeded during impregnation,much more expensive however. UV protection with polyurethane paint. Another small detail once dried it is more difficult to sand.

3)Vinylester resin

Its skills are between the polyester resin and the epoxy resin, the price too. May be laminated on the polyester , and like polyester resin we use mat fabrics.

4) Gelcoat

This is a resin made with different loads, it protects the laminate and gives a smooth final shape; in general it is pre-accelerated and hardens with a catalyst. The most of time it is white to reflect sunlight and UV for a better protection, can however add a coloring agent to give it a chosen color. There are gelcoats used in molds without paraffin and gelcoats for repair or application on the hull with paraffin(allows the gelcoat to dry in the open air).

5)Main equipment

when we work with resin we have always to foresee a little electronic scale to know precisely our quantities and a gradual pipette to have balanced mixtures, plastic bottle bottoms dry and hands and eyes protections. Against styrene gaz always wear a mask .

6)Osmosis

This is the main problem met by polyester hulls when it gets older. The detection signs are simple to notice: small blisters on the hull, vinegar scent(acetic acid) in the bilges, acetic acid can be detected when blisters are drilled. Osmosis is a chemical reaction, it is easily explained by taking the case(not very funky I admit)of a wrecked man with a lack of freshwater who drink salt water(beuark!).

Drinking water rich in salt dehydrates, because of the cell skins. This is a semi-permeable membrane which protects the molecules of the cell, it lets pass the molecules necessary for life but it's a dam for others. In fact just small molecules can cross the membrane only(oxygen, carbon dioxide, freshwater…)and large molecules(ions of the dissolved salt in the water)can not pass. If the solutions on both sides of a semi-permeable membrane have the same concentration, system is balanced and molecules will stay on their place. If concentrations are unequal, then water molecules pass from one side to an other of the membrane to restore balance, it's osmosis. So the salt water absorption creates more salt concentration on the surroundings than into the cell, to restore a balanced system the cell will “give” water to extracellular surroundings, and dehydrate(a freshwater fish dropped in the sea dies from dehydration).

For polyester hulls it is a bit the same idea, Water invades polyester and slowly destroys the resin. Why? because during the manufacture of the resin little cavities full of acid liquid are created, it happens that the catalyst used was not fully permeated all corners of the fiber. Finally in that case some water manage to cross gelcoat(the semi-permeable membrane)to decrease the acid liquid concentration in the blister. with hydrolysis there will be acetic acid, and the volume of water increases and can not get out. As fresh water is less concentrated in ions than seawater, then the osmosis reactions are even greater with freshwater(lakes, rivers).

Corrosion under seawater

On the sea, the material is severely tested by seawater for the careen and salt air for topsides. Their slow and gradual chemical action on metal cause corrosion.

1)Voltaic pile working

Invented by Alessandro Volta, it consisted of a stack of alternating discs of zinc and copper separated by paperboard soaked in salt water.

Pila_di_Volta_01

The negative terminal is a zinc disc(anode)and the positive terminal is a copper disk(cathode). The electrolyte in this case is the impregnated salt water paperboard. The voltage creates an electrons motion, zinc will be corroded(it is always anode which will be corroded)and electrons lost by zinc will go on cathode(here, copper). It is a redox reaction in which zinc is the reductant and copper oxidant . To summarize a zinc atom loses two electrons migrated on copper, next to the cathode these electrons , through a reduction reaction will create dihydrogen(2H20 and 2é give 2OH- and H2).

Roughly the same story in seawater. By immersing a copper plate and a zinc plate close each other, zinc corrodes itself. Here sea water acts as the electrolyte. The phenomenon is accelerated by voltage between those two plates or by increasing the temperature of water. This is why we must focus our attention on electric power losses on aluminum boats. By taking two different kind of metals, for example aluminum and bronze, we see the same principle with the aluminum which corrodes itself(to install a bronze valve on an aluminum hull…be careful!).

2) Strong / weak metals

the metal role(cathode or anode)isn't fixed, it depends on the metal nature which it is associated by direct or indirect link(salt air, salt water). Here is a list of metals from the more resistant to the weakest against galvanic corrosion:

Stainless steel, Nickel, Bronze, Bronze / aluminum alloy, Copper, brass, Lead, cast iron, Steel, Aluminium alloy, Aluminium and Zinc at the end.

(Notice: Stainless steel A4 type is the one to use in marine environment)

With that you can foresee in the marine environment “who will eat who”:

For example by combining Nickel with Brass, the anode is the Brass. By combining the cast iron with Steel, the anode will be steel. The more a large gap between two metals is in this list and the more galvanic effects will be important(Inox and Zinc=Bingo!).

3)Precautions

For two metal things in contact:

corrosion

For example, we take an aluminium mast("support")where we want to fix a stainless steel plate(example the spi pole ring). connections must be of the same metal as the object set(by a stainless steel rivet for example), and the plate must always be isolated from the support by an elastomeric sealant( sika type). Otherwise, welcome damages! Connexion(rivet, screw)must also be isolated from the support(elastomeric sealant for rivet and grease for screw ). Always take care to trim the drilled holes and clean the contact areas before setting, you have to avoid stainless steel turnings under the plate, causing corrosion by puncture(also avoid scratches on parts).

For two parts of the same metal, it should also be isolated by a mastic. If the plate is not chamfered, you must do a chamfer in elastomeric sealant around the plate to avoid water entrances(differential aeration corrosion).

4)Anodes

From what we have seen, metal parts on a boat are subject to electrolytic phenomena, So touched by progressive destruction. To avoid this kind of fuses are used on board, it's anodes. It will be destroyed instead of the metal parts of the boat. These anodes must have to be changed regularly. They are made of either aluminum / Zinc alloy or Aluminum(weakest metals listed just above). From what we have seen in the number 2 paragraph, aluminum anodes last longer in time, they also provide better protection. Anodes protect the hull, propeller, Propeller shaft, the inboard engine. On freshwater anodes used are in aluminium, On the sea ​​we rather use alu/zinc alloy anodes.

Ropes

Old natural fiber ropes had many drawbacks, they swelled with moisture and lost their resistance, rotted or got moldy. Their weight / strength ratio was poor, making them bulky. In addition they could injure sailor's hands especially in cold weather(example: papyrus, Coconut fiber, hemp fiber, sisal…). Fortunately things have changed!

1)First synthetic ropes

.Polyamide(nylon): it comes from the coal process. when you are burning this kind of fiber it smells like celery and you see a white smoke, it is used for mooring ropes and anchor lines because it's resilient .

.Polyester: it comes from oil, its flame creates a black smoke. Less distendable than the polyamide, it may even be non-deformable after treatment(prestretching)in manufacturing . It is therefore useful for ropes where slack on it may be bad(ex: halyards). It is widely used to make sheaths on Kevlar or spectra souls.

.Polypropylene: comes from oil too, it smells like wax being consumed. This is the weakest of the three but also the cheapest, and it has the skill to float . It can be used as moorings but it is mostly used for safety gear(ex: rope for the horseshoe buoy linked with the floating light in case of man overboard).

2)New synthetic ropes

.Polyethylene: white colored it smells like wax when it's burning. Its good ratio weight / strength allows weight's reductions on the rigging, particularly on the top(spectra, dyneema).

.Aramidic fiber(kevlar): yellow/beige colored, unable to melge. However he fears abrasion and U.V, it is necessary to use it under sheath to protect it. It is used for halyards, runners and spinnaker guy.

.LPC(vectran): it is yellow and is used to make many textile shackles and fasteners.

.PBO(zylon): yellow colored. under sheath, is used to make shrouds.

3)Words used for ropes

.Density: it is the floating ability, as the water's density = 1, if the rope has a density<1 it will float. Otherwise it will sink .

.Tenacity: snapping resistance.

.Creep(I guess in English...: this is irreversible's elongation under a steady load.

.Ingress of humidity: is the water's amount retained by the fiber after immersion(gived in %).

About the snapping load there are abacus used in rope's choice, we can also use this formula:

Tension=S*V^2*0,02104(S = sail's surface, V = wind speed in knots, Tension in kg).

For cruises the average tension has to be multiplied by 4. Use of the rope is done at 25% of its snapping load. For competition we look for a use with a higher percentage on snapping load, simply just to gain weight.

4)Ropes length

Generally we count at least length used with three turns around the winch and 1,5 m of sleeping part, then add 1.5 / 2m at the ideal length to overlap the ends that will tire in the knots after a certain time.

.The mainsheet: it is measured by the ratio used, it should not be longer than the mark used when you are running downwind(length's limit is where, as soon as we have eased off, the boom touches the leeward shrouds)plus the necessary length to manoeuver when you are sat windward.

(Notice: for a mainsail's tackle, The multiplication ratio of mainsheet is equal to the number of outgoing strands from the tackle, only tackle's part which is moving)

.Mainsail's halyard: it must be fixed on the deck when it's not used with at least a sleeping part of 2 meters after the jam cleat exit.

.The mainsheet traveller: being eased off downwind it has nevertheless to be used easily when you are hiking.

.The topping lift: it must be linked on the spi pole when this one is laying on the deck, and it must pass on the mast foot too, and allow free passage of the jib sheet.

Reefing line: they must be long enough to be set up on the mainsail when it's all hoisted, or at least for the first and the second reefing line(but all the reefing lines is better especially with a reduced crew).

.Spi guy and spi sheet: about twice the length of the boat and one meter.

.Jib sheet: with a spi pole in use it must pass in front of the topping lift, above the pole and return to cockpit.

5)Whippings and splices

A knot on a rope brings a loss about 50% of its snapping load. There is nevertheless a solution for that: splices. They are done on the hawsers ends(splices on three strands hawsers are the easiest to do)and halyard ends mainly(slightly more difficult).

epissure3torons

splice on a three-strand hawser.

Whippings protect rope's ends from damages, heat-shrinkable sleeves may also be used instead (same thing as the heat-shrinkable sheaths used in electricity)if you are not a sewing fan. It is useful to do whippings on every rope's ends onboard. The whipping wire is a fatty wire, an efficient skill needful to have a motionless wire during our sewing work, when the whipping is done we heat it with a lighter to finish the work. Here's an example of a whipping sewn on the three strands(it is better to always do sewn whippings, they are more resistant).

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